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Bai, Wenyuan, Xinhui Zhang, Zhen Gao, Shuyu Xie, Ke Peng und Yu Chen. „Sensorless Coestimation of Temperature and State-of-Charge for Lithium-Ion Batteries Based on a Coupled Electrothermal Model“. International Journal of Energy Research 2023 (06.02.2023): 1–18. http://dx.doi.org/10.1155/2023/4021256.
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Accurate estimations of the temperature and the state-of-charge (SOC) are of extreme importance for the safety of lithium-ion battery operation. Traditional battery temperature and SOC estimation methods often omit the relation between battery temperature and SOC, which may lead to significant errors in the estimations. This study presents a coupled electrothermal battery model and a coestimation method for simultaneously estimating the temperature and SOC of lithium-ion batteries. The coestimation method is performed by a coupled model-based dual extended Kalman filter (DEKF). The coupled estimators utilizing electrochemical impedance spectroscopy (EIS) measurements, rather than utilizing direct battery surface measurements, are adopted to estimate the battery temperature and SOC, respectively. The information being exchanged between the temperature estimator and the SOC estimator effectively improves the estimation accuracy. Extensive experiments show that, in contrast with the EKF-based separate estimation method, the DEKF-based coestimation method is more favorable in reducing errors for estimating both the temperature and SOC even if the battery core temperature has increased by 17°C or more during the process of test.
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IRFAGUTAMI, NI PUTU NIA, I. GUSTI AYU MADE SRINADI und I. WAYAN SUMARJAYA. „PERBANDINGAN REGRESI ROBUST PENDUGA MM DENGAN METODE RANDOM SAMPLE CONSENSUS DALAM MENANGANI PENCILAN“. E-Jurnal Matematika 3, Nr. 2 (31.05.2014): 45. http://dx.doi.org/10.24843/mtk.2014.v03.i02.p065.
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The presence of outliers in observation can result in biased in parameter estimation using ordinary least square (OLS). Robust regression MM-estimator is one of the estimations methods that able to obtain a robust estimator against outliers. Random sample consensus (ransac) is another method that can be used to construct a model for observations data and also estimating a robust estimator against outliers. Based on the study, ransac obtained model with less biased estimator than robust regression MM-estimator.
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Thanoon, Shaymaa Riyadh. „A comparison between Bayes estimation and the estimation of the minimal unbiased quadratic Standard of the bi-division variance analysis model in the presence of interaction“. Tikrit Journal of Pure Science 25, Nr. 2 (17.03.2020): 116. http://dx.doi.org/10.25130/j.v25i2.966.
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In this study, the variance compounds parameters of the mixed bi-division variance analysis sample are estimated. This estimation is obtained, by Bayes quadratic unbiased estimator. The second way to estimate variance compounds parameters of a suggested tow-way analysis of variance mixed model with interaction. estimation is done out by the approach called (MINQUÉ). The estimation approach is conducted on true obtained from departments at the college of agriculture/university of Mosul. These data represent the development of growing various kinds of tomato so that the development represents three factors: the first is tomato kind, this is the first factor (H) and the factor of natural fertilizer rate, and this is the second factor (M), and the interaction between the two factors (HM). A random sample is taken from these data in order to get the random linear sample. The elementary values estimated by Bayes unbiased estimator are very much close to those estimated by variance analysis style when compared with the estimated values of the variance estimation parameters done by minimum standard quadratic unbiased estimation. The elementary values represent random linear sample parameters used to estimate minimum quadratic unbiased standard. The elementary values of the estimations are also obtained via analyzing bi-division variance, then these estimations are employed in estimating minimum quadratic unbiased standard. the estimation results by Bayes approach are very similar to those done by variance analysis
http://dx.doi.org/10.25130/tjps.25.2020.038
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Liu, Bing, Zhen Chen, Xiangdong Liu und Fan Yang. „An Efficient Nonlinear Filter for Spacecraft Attitude Estimation“. International Journal of Aerospace Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/540235.
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Increasing the computational efficiency of attitude estimation is a critical problem related to modern spacecraft, especially for those with limited computing resources. In this paper, a computationally efficient nonlinear attitude estimation strategy based on the vector observations is proposed. The Rodrigues parameter is chosen as the local error attitude parameter, to maintain the normalization constraint for the quaternion in the global estimator. The proposed attitude estimator is performed in four stages. First, the local attitude estimation error system is described by a polytopic linear model. Then the local error attitude estimator is designed with constant coefficients based on the robustH2filtering algorithm. Subsequently, the attitude predictions and the local error attitude estimations are calculated by a gyro based model and the local error attitude estimator. Finally, the attitude estimations are updated by the predicted attitude with the local error attitude estimations. Since the local error attitude estimator is with constant coefficients, it does not need to calculate the matrix inversion for the filter gain matrix or update the Jacobian matrixes online to obtain the local error attitude estimations. As a result, the computational complexity of the proposed attitude estimator reduces significantly. Simulation results demonstrate the efficiency of the proposed attitude estimation strategy.
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Wu, Renzhi, Bolin Ding, Xu Chu, Zhewei Wei, Xiening Dai, Tao Guan und Jingren Zhou. „Learning to be a statistician“. Proceedings of the VLDB Endowment 15, Nr. 2 (Oktober 2021): 272–84. http://dx.doi.org/10.14778/3489496.3489508.
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Estimating the number of distinct values (NDV) in a column is useful for many tasks in database systems, such as columnstore compression and data profiling. In this work, we focus on how to derive accurate NDV estimations from random (online/offline) samples. Such efficient estimation is critical for tasks where it is prohibitive to scan the data even once. Existing sample-based estimators typically rely on heuristics or assumptions and do not have robust performance across different datasets as the assumptions on data can easily break. On the other hand, deriving an estimator from a principled formulation such as maximum likelihood estimation is very challenging due to the complex structure of the formulation. We propose to formulate the NDV estimation task in a supervised learning framework, and aim to learn a model as the estimator. To this end, we need to answer several questions: i) how to make the learned model workload agnostic; ii) how to obtain training data; iii) how to perform model training. We derive conditions of the learning framework under which the learned model is workload agnostic , in the sense that the model/estimator can be trained with synthetically generated training data, and then deployed into any data warehouse simply as, e.g. , user-defined functions (UDFs), to offer efficient (within microseconds on CPU) and accurate NDV estimations for unseen tables and workloads. We compare the learned estimator with the state-of-the-art sample-based estimators on nine real-world datasets to demonstrate its superior estimation accuracy. We publish our code for training data generation, model training, and the learned estimator online for reproducibility.
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Sugiyama, Masashi, Takafumi Kanamori, Taiji Suzuki, Marthinus Christoffel du Plessis, Song Liu und Ichiro Takeuchi. „Density-Difference Estimation“. Neural Computation 25, Nr. 10 (Oktober 2013): 2734–75. http://dx.doi.org/10.1162/neco_a_00492.
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We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure of first estimating two densities separately and then computing their difference. However, this procedure does not necessarily work well because the first step is performed without regard to the second step, and thus a small estimation error incurred in the first stage can cause a big error in the second stage. In this letter, we propose a single-shot procedure for directly estimating the density difference without separately estimating two densities. We derive a nonparametric finite-sample error bound for the proposed single-shot density-difference estimator and show that it achieves the optimal convergence rate. We then show how the proposed density-difference estimator can be used in L2-distance approximation. Finally, we experimentally demonstrate the usefulness of the proposed method in robust distribution comparison such as class-prior estimation and change-point detection.
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Talakua, Mozart W., und Jefri Tipka. „ESTIMASI PARAMETER DISTRIBUSI EKPONENSIAL PADA LOKASI TERBATAS“. BAREKENG: Jurnal Ilmu Matematika dan Terapan 1, Nr. 2 (01.12.2007): 1–7. http://dx.doi.org/10.30598/barekengvol1iss2pp1-7.
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The common method in Estimating Parameter Distribution Exponential at Finite Location is Maximum Likelihood Estimation (MLE).The best estimator is consistent estimator. Because of The Mean Square Error (MSE) can be used in comparing some detectable estimators that it had looking for with Maximum Likelihood Estimation (MLE) so can find the consistent estimator in Estimating Parameter Distribution Exponential At Finite Location
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Chamidah, Nur, Budi Lestari, I. Nyoman Budiantara und Dursun Aydin. „Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator“. Symmetry 16, Nr. 4 (25.03.2024): 386. http://dx.doi.org/10.3390/sym16040386.
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In data analysis using a nonparametric regression approach, we are often faced with the problem of analyzing a set of data that has mixed patterns, namely, some of the data have a certain pattern and the rest of the data have a different pattern. To handle this kind of datum, we propose the use of a mixed estimator. In this study, we theoretically discuss a developed estimation method for a nonparametric regression model with two or more response variables and predictor variables, and there is a correlation between the response variables using a mixed estimator. The model is called the multiresponse multipredictor nonparametric regression (MMNR) model. The mixed estimator used for estimating the MMNR model is a mixed estimator of smoothing spline and Fourier series that is suitable for analyzing data with patterns that partly change at certain subintervals, and some others that follow a recurring pattern in a certain trend. Since in the MMNR model there is a correlation between responses, a symmetric weight matrix is involved in the estimation process of the MMNR model. To estimate the MMNR model, we apply the reproducing kernel Hilbert space (RKHS) method to penalized weighted least square (PWLS) optimization for estimating the regression function of the MMNR model, which consists of a smoothing spline component and a Fourier series component. A simulation study to show the performance of proposed method is also given. The obtained results are estimations of the smoothing spline component, Fourier series component, MMNR model, weight matrix, and consistency of estimated regression function. In conclusion, the estimation of the MMNR model using the mixed estimator is a combination of smoothing spline component and Fourier series component estimators. It depends on smoothing and oscillation parameters, and it has linear in observation and consistent properties.
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Zerdali, Emrah, und Murat Barut. „Extended Kalman Filter Based Speed-Sensorless Load Torque and Inertia Estimations with Observability Analysis for Induction Motors“. Power Electronics and Drives 3, Nr. 1 (01.12.2018): 115–27. http://dx.doi.org/10.2478/pead-2018-0002.
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Abstract This paper aims to introduce a novel extended Kalman filter (EKF) based estimator including observability analysis to the literature associated with the high performance speed-sensorless control of induction motors (IMs). The proposed estimator simultaneously performs the estimations of stator stationary axis components of stator currents and rotor fluxes, rotor mechanical speed, load torque including the viscous friction term, and reciprocal of total inertia by using measured stator phase currents and voltages. The inertia estimation is done since it varies with the load coupled to the shaft and affects the performance of speed estimation especially when the rotor speed changes. In this context, the estimations of all mechanical state and parameters besides flux estimation required for high performance control methods are performed together. The performance of the proposed estimator is tested by simulation and real-time experiments under challenging variations in load torque and velocity references; and in both transient and steady states, the quite satisfactory estimation performance is achieved.
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Note, Yuya, Masahito Watanabe, Hiroaki Yoshimura, Takaharu Yaguchi und Toshiaki Omori. „Sparse Estimation for Hamiltonian Mechanics“. Mathematics 12, Nr. 7 (25.03.2024): 974. http://dx.doi.org/10.3390/math12070974.
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Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.
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Baran Kaya, Tuğba, und Sedef Çelik Demirci. „Examination of the Estimation Skills and Strategies of Pre-Service Elementary Mathematics Teachers“. International Journal of Research in Education and Science 8, Nr. 2 (22.05.2022): 243–61. http://dx.doi.org/10.46328/ijres.2897.
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The present study aimed to determine the estimation skills of elementary education pre-service mathematics teachers and the strategies they adopt in estimation. The case study methodology was employed in the study, and the participants included 37 volunteering students attending the fourth grade in the Primary Education Mathematics Instruction Department at a university located in the Central Anatolia Region in Turkey. The study data were collected with an 8-item Estimation Strategy Test developed by the authors. The test included numerosity, computational, and measurement estimation questions. In addition to making estimations, the students were asked to write the reasons behind their estimations. The descriptive analysis technique was employed to analyze the study data, and the data were coded based on the estimation strategies adopted by the pre-service teachers and similarity of their estimations with the actual values. The data are presented as MAXQDA maps, and excerpts from student responses are also presented. The study findings demonstrated that the responses of most pre-service teachers were similar to the actual value in computational estimations; however, numerosity or measurement estimations were not similar. Furthermore, certain pre-service teachers inclined to conduct the actual operation instead of estimating the results during computational estimation, and directly counted the results in numerosity estimation. Also, it was determined that a significant number of pre-service teachers made computational errors in numerosity and computational estimation.
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Gao, Chao, Guorong Zhao, Jianhua Lu und Shuang Pan. „Decentralized state estimation for networked spatial-navigation systems with mixed time-delays and quantized complementary measurements: The moving horizon case“. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 232, Nr. 11 (08.06.2017): 2160–77. http://dx.doi.org/10.1177/0954410017712277.
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In this paper, the navigational state estimation problem is investigated for a class of networked spatial-navigation systems with quantization effects, mixed time-delays, and network-based observations (i.e. complementary measurements and regional estimations). A decentralized moving horizon estimation approach, featuring complementary reorganization and recursive procedure, is proposed to tackle this problem. First, through the proposed reorganized scheme, a random delayed system with complementary observations is reconstructed into an equivalent delay-free one without dimensional augment. Second, with this equivalent system, a robust moving horizon estimation scheme is presented as a uniform estimator for the navigational states. Third, for the demand of real-time estimate, the recursive form of decentralized moving horizon estimation approach is developed. Furthermore, a collective estimation is obtained through the weighted fusion of two parts, i.e. complementary measurements based estimation, and regional estimations directly from the neighbors. The convergence properties of the proposed estimator are also studied. The obtained stability condition implicitly establishes a relation between the upper bound of the estimation error and two parameters, i.e. quantization density and delay occur probability. Finally, an application example to networked unmanned aerial vehicles is presented and comparative simulations demonstrate the main features of the proposed method.
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Blackburne, Edward F., und Mark W. Frank. „Estimation of Nonstationary Heterogeneous Panels“. Stata Journal: Promoting communications on statistics and Stata 7, Nr. 2 (Juni 2007): 197–208. http://dx.doi.org/10.1177/1536867x0700700204.
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We introduce a new Stata command, xtpmg, for estimating nonstationary heterogeneous panels in which the number of groups and number of time-series observations are both large. Based on recent advances in the nonstationary panel literature, xtpmg provides three alternative estimators: a traditional fixed-effects estimator, the mean-group estimator of Pesaran and Smith (Estimating long-run relationships from dynamic heterogeneous panels, Journal of Econometrics 68: 79–113), and the pooled mean-group estimator of Pesaran, Shin, and Smith (Estimating long-run relationships in dynamic heterogeneous panels, DAE Working Papers Amalgamated Series 9721; Pooled mean group estimation of dynamic heterogeneous panels, Journal of the American Statistical Association 94: 621–634).
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Rodríguez-García, Marco A., Isaac Pérez Castillo und P. Barberis-Blostein. „Efficient qubit phase estimation using adaptive measurements“. Quantum 5 (04.06.2021): 467. http://dx.doi.org/10.22331/q-2021-06-04-467.
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Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is given by the so-called quantum Cramér-Rao bound, so any measurement strategy aims to obtain estimations as close as possible to it. However, more often than not, the current state-of-the-art methods to estimate quantum phases fail to reach this bound as they rely on maximum likelihood estimators of non-identifiable likelihood functions. In this work we thoroughly review various schemes for estimating the phase of a qubit, identifying the underlying problem which prohibits these methods to reach the quantum Cramér-Rao bound, and propose a new adaptive scheme based on covariant measurements to circumvent this problem. Our findings are carefully checked by Monte Carlo simulations, showing that the method we propose is both mathematically and experimentally more realistic and more efficient than the methods currently available.
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Capretz, Luiz Fernando, und Venus Marza. „Improving Effort Estimation by Voting Software Estimation Models“. Advances in Software Engineering 2009 (01.09.2009): 1–8. http://dx.doi.org/10.1155/2009/829725.
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Estimating software development effort is an important task in the management of large software projects. The task is challenging, and it has been receiving the attentions of researchers ever since software was developed for commercial purpose. A number of estimation models exist for effort prediction. However, there is a need for novel models to obtain more accurate estimations. The primary purpose of this study is to propose a precise method of estimation by selecting the most popular models in order to improve accuracy. Consequently, the final results are very precise and reliable when they are applied to a real dataset in a software project. Empirical validation of this approach uses the International Software Benchmarking Standards Group (ISBSG) Data Repository Version 10 to demonstrate the improvement in software estimation accuracy.
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Salha, Raid B., Hazem I. El Shekh Ahmed und Hossam O. EL-Sayed. „Adaptive Kernel Estimation of the Conditional Quantiles“. International Journal of Statistics and Probability 5, Nr. 1 (22.12.2015): 79. http://dx.doi.org/10.5539/ijsp.v5n1p79.
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In this paper, we define the adaptive kernel estimation of the conditional distribution function (cdf) for independent and identically distributed (iid) data using varying bandwidth. The bias, variance and the mean squared error of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated.<br /><br />The results of the simulation study show that the adaptive kernel estimation of the conditional quantiles with varying bandwidth have better performance than the kernel estimations with fixed bandwidth.
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Sasaki, Hiroaki, Yung-Kyun Noh, Gang Niu und Masashi Sugiyama. „Direct Density Derivative Estimation“. Neural Computation 28, Nr. 6 (Juni 2016): 1101–40. http://dx.doi.org/10.1162/neco_a_00835.
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Estimating the derivatives of probability density functions is an essential step in statistical data analysis. A naive approach to estimate the derivatives is to first perform density estimation and then compute its derivatives. However, this approach can be unreliable because a good density estimator does not necessarily mean a good density derivative estimator. To cope with this problem, in this letter, we propose a novel method that directly estimates density derivatives without going through density estimation. The proposed method provides computationally efficient estimation for the derivatives of any order on multidimensional data with a hyperparameter tuning method and achieves the optimal parametric convergence rate. We further discuss an extension of the proposed method by applying regularized multitask learning and a general framework for density derivative estimation based on Bregman divergences. Applications of the proposed method to nonparametric Kullback-Leibler divergence approximation and bandwidth matrix selection in kernel density estimation are also explored.
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Al-Omari, Amer Ibrahim, SidAhmed Benchiha und Ibrahim M. Almanjahie. „Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design“. Mathematics 10, Nr. 17 (02.09.2022): 3170. http://dx.doi.org/10.3390/math10173170.
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An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study.
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Adhya, Sumanta. „Bootstrap Variance Estimation for Semiparametric Finite Population Distribution Function Estimator“. Calcutta Statistical Association Bulletin 70, Nr. 1 (Mai 2018): 17–32. http://dx.doi.org/10.1177/0008068318765583.
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Estimating finite population distribution function (FPDF) emerges as an important problem to the survey statisticians since the pioneering work of Chambers and Dunstan [1] . It unifies estimation of standard finite population parameters, namely, mean and quantiles. Regarding this, estimating variance of FPDF estimator is an important task for accessing the quality of the estimtor and drawing inferences (e.g., confidence interval estimation) on finite population parameters. Due to non-linearity of FPDF estimator, resampling-based methods are developed earlier for parametric or non-parametric Chambers–Dunstan estimator. Here, we attempt the problem of estimating variance of P-splines-based semiparametric model-based Chambers–Dunstan type estimator of the FPDF. The proposed variance estimator involes bootstrapping. Here, the bootstrap procedure is non-trivial since it does not imitate the full mechanism of two-stage sample generating procedure from an infinite hypothetical population (superpopulation). We have established the weak consistency of the proposed resampling-based variance estimator for specific sampling designs, e.g., simple random sampling. Also, the satisfactory empirical performance of the poposed estimator has been shown through simulation studies and a real life example.
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Ran, Mengfei, und Yihe Yang. „Optimal Estimation of Large Functional and Longitudinal Data by Using Functional Linear Mixed Model“. Mathematics 10, Nr. 22 (17.11.2022): 4322. http://dx.doi.org/10.3390/math10224322.
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The estimation of large functional and longitudinal data, which refers to the estimation of mean function, estimation of covariance function, and prediction of individual trajectory, is one of the most challenging problems in the field of high-dimensional statistics. Functional Principal Components Analysis (FPCA) and Functional Linear Mixed Model (FLMM) are two major statistical tools used to address the estimation of large functional and longitudinal data; however, the former suffers from a dramatically increasing computational burden while the latter does not have clear asymptotic properties. In this paper, we propose a computationally effective estimator of large functional and longitudinal data within the framework of FLMM, in which all the parameters can be automatically estimated. Under certain regularity assumptions, we prove that the mean function estimation and individual trajectory prediction reach the minimax lower bounds of all nonparametric estimations. Through numerous simulations and real data analysis, we show that our new estimator outperforms the traditional FPCA in terms of mean function estimation, individual trajectory prediction, variance estimation, covariance function estimation, and computational effectiveness.
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Hahn, Andreas, Ulrike Loderstädt, Hagen Frickmann und Norbert G. Schwarz. „Sparing the control arm using well-characterized diagnostic approaches – the Gart and Buck prevalence estimator for efficacy estimation in single-arm trials“. Journal of Laboratory Medicine 43, Nr. 5 (25.10.2019): 279–81. http://dx.doi.org/10.1515/labmed-2019-0091.
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Abstract Efficacy estimation of medical interventions in clinical trials requires diagnostics to assess the study endpoint. The imperfect nature of diagnostics often leads to biased efficacy estimations, usually underestimation, that could result in failure of clinical trials. Adjustment methods can be used if sensitivity and specificity are known, but they are not regularly applied. Double-arm clinical trials are the standard for demonstrating the superiority of a medical intervention. However, sometimes single-arm trials are the only option: for example, if a parallel group trial design with a control group is regarded as unethical. Based on the Gart and Buck prevalence estimator (aka the Rogan-Gladen estimator), we demonstrate how the concept of diagnostic accuracy-adjusted effect estimation can be used for estimating the efficacy in single-arm trials. The accuracy of the diagnostic measure (sensitivity and specificity) used for endpoint assessment as well as the predictive accuracy of a predictor and its allocation among the study population have to be known to obtain consistent efficacy estimation of a medical intervention. If double-arm trials are not feasible, an approach such as that described here can provide evidence regarding the efficacy of a medical intervention based on a single-arm trial.
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Saikkonen, Pentti. „Asymptotically Efficient Estimation of Cointegration Regressions“. Econometric Theory 7, Nr. 1 (März 1991): 1–21. http://dx.doi.org/10.1017/s0266466600004217.
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An asymptotic optimality theory for the estimation of cointegration regressions is developed in this paper. The theory applies to a reasonably wide class of estimators without making any specific assumptions about the probability distribution or short-run dynamics of the data-generating process. Due to the nonstandard nature of the estimation problem, the conventional minimum variance criterion does not provide a convenient measure of asymptotic efficiency. An alternative criterion, based on the concentration or peakedness of the limiting distribution of an estimator, is therefore adopted. The limiting distribution of estimators with maximum asymptotic efficiency is characterized in the paper and used to discuss the optimality of some known estimators. A new asymptotically efficient estimator is also introduced. This estimator is obtained from the ordinary least-squares estimator by a time domain correction which is nonparametric in the sense that no assumption of a finite parameter model is required. The estimator can be computed with least squares without any initial estimations.
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Liu, Jie, Wenqian Dong, Qingqing Zhou und Dong Li. „Fauce“. Proceedings of the VLDB Endowment 14, Nr. 11 (Juli 2021): 1950–63. http://dx.doi.org/10.14778/3476249.3476254.
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Cardinality estimation is a fundamental and critical problem in databases. Recently, many estimators based on deep learning have been proposed to solve this problem and they have achieved promising results. However, these estimators struggle to provide accurate results for complex queries, due to not capturing real inter-column and inter-table correlations. Furthermore, none of these estimators contain the uncertainty information about their estimations. In this paper, we present a join cardinality estimator called Fauce. Fauce learns the correlations across all columns and all tables in the database. It also contains the uncertainty information of each estimation. Among all studied learned estimators, our results are promising: (1) Fauce is a light-weight estimator, it has 10× faster inference speed than the state of the art estimator; (2) Fauce is robust to the complex queries, it provides 1.3×--6.7× smaller estimation errors for complex queries compared with the state of the art estimator; (3) To the best of our knowledge, Fauce is the first estimator that incorporates uncertainty information for cardinality estimation into a deep learning model.
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Arahal, Manuel R., Alfredo Pérez Vega-Leal, Manuel G. Satué und Sergio Esteban. „Assessing SOC Estimations via Reverse-Time Kalman for Small Unmanned Aircraft“. Energies 17, Nr. 20 (17.10.2024): 5161. http://dx.doi.org/10.3390/en17205161.
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This paper presents a method to validate state of charge (SOC) estimations in batteries for their use in remotely manned aerial vehicles (UAVs). The SOC estimation must provide the mission control with a measure of the available range of the aircraft, which is critical for extended missions such as search and rescue operations. However, the uncertainty about the initial state and depth of discharge during the mission makes the estimation challenging. In order to assess the estimation provided to mission control, an a posteriori re-estimation is performed. This allows for the assessment of estimation methods. A reverse-time Kalman estimator is proposed for this task. Accurate SOC estimations are crucial for optimizing the utilization of multiple UAVs in a collaborative manner, ensuring the efficient use of energy resources and maximizing mission success rates. Experimental results for LiFePO4 batteries are provided, showing the capabilities of the proposal for the assessment of online SOC estimators.
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Williams, Michael S. „Improved estimation of domain totals in forest surveys“. Canadian Journal of Forest Research 25, Nr. 7 (01.07.1995): 1203–7. http://dx.doi.org/10.1139/x95-133.
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The literature on estimating population totals in forest surveys is well developed. However in most practical applications, estimation of subpopulation totals (historically referred to as domains of study) is of equal or greater importance but receives much less attention. In this paper, techniques for estimating totals and variances for domains of study are reviewed and an adjusted estimator, with improved efficiency, is derived for estimating such totals. The properties of the adjusted and traditional estimator were studied using two populations, where each population contained three domains of study. In a simulation study based on probability proportional to size sampling, the adjusted estimator produced standard errors that ranged between 23 and 64% of those of the traditional estimator. No detectable bias of the new estimator was found when estimating the most common domains of study. Some bias was evident for estimates of rare domains of study. A bootstrap variance estimator for both the adjusted and unadjusted estimator produced somewhat biased estimates of the variance for the rare domains of study, with biases ranging between−18.2 and 30.8%.
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Roesch, Francis A. „Compatible Estimators of the Components of Change for a Rotating Panel Forest Inventory Design“. Forest Science 53, Nr. 1 (01.02.2007): 50–61. http://dx.doi.org/10.1093/forestscience/53.1.50.
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Abstract This article presents two approaches for estimating the components of forest change utilizing data from a rotating panel sample design. One approach uses a variant of the exponentially weighted moving average estimator and the other approach uses mixed estimation. Three general transition models were each combined with a single compatibility model for the mixed estimation approach. The four resulting estimation systems are compared and contrasted in a sample simulation study covering four simulated populations.
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admin, admin. „On The Bayesian Estimation of Parameters of SQDM“. Neutrosophic and Information Fusion 3, Nr. 1 (2024): 34–41. http://dx.doi.org/10.54216/nif.030105.
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This work is concerned with the problem of estimating parameters of spatial quadratic models by Bayesian technique (SQDM). This technique involves the prior information of the first and second moment of the parameters, where its estimation model is called the Bayesian quadratic unbiased estimator. The results of the estimation are taken in compared with the estimates of minimum norm quadratic unbiased estimators.
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Fitrianto, Anwar, und Sim Hui Xin. „COMPARISONS BETWEEN ROBUST REGRESSION APPROACHES IN THE PRESENCE OF OUTLIERS AND HIGH LEVERAGE POINTS“. BAREKENG: Jurnal Ilmu Matematika dan Terapan 16, Nr. 1 (21.03.2022): 243–52. http://dx.doi.org/10.30598/barekengvol16iss1pp241-250.
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The study aimed to compare a few robust approaches in linear regression in the presence of outlier and high leverage points. Ordinary least square (OLS) estimation of parameters is the most basic approach practiced widely in regression analysis. However, some fundamental assumptions must be fulfilled to provide good parameter estimates for the OLS estimation. The error term in the regression model must be identically and independently comes from a Normal distribution. The failure to fulfill the assumptions will result in a poor estimation of parameters. The violation of assumptions may occur due to the presence of unusual observations (which is known as outliers or high leverage points. Even in the case of only one single extreme value appearing in the set of data, the result of the OLS estimation will be affected. The parameter estimates may become bias and unreliable if the data contains outlier or high leverage point. In order to solve the consequences due to unusual observations, robust regression is suggested to help in reducing the effect of unusual observation to the result of estimation. There are four types of robust regression estimations practiced in this paper: M estimation, LTS estimation, S estimation, and MM estimation, respectively. Comparisons of the result among different types of robust estimator and the classical least square estimator have been carried out. M estimation works well when the data is only contaminated in response variable. But in the case of presence of high leverage point, M estimation cannot perform well.
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Chen, Jia, und Junke Kou. „Pointwise Estimation of Anisotropic Regression Functions Using Wavelets with Data-Driven Selection Rule“. Mathematics 12, Nr. 1 (27.12.2023): 98. http://dx.doi.org/10.3390/math12010098.
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This paper considers pointwise estimations of anisotropic regression functions. We firstly construct a linear wavelet estimator and study the convergence rate of this estimator in anisotropic Besov spaces. In order to obtain an adaptive estimator, a regression estimator is proposed with a scaling parameter data-driven selection rule. It turns out that our results attain the optimal convergence rate of nonparametric pointwise estimation.
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Shadmehr, Reza, und David Z. D'Argenio. „A Neural Network for Nonlinear Bayesian Estimation in Drug Therapy“. Neural Computation 2, Nr. 2 (Juni 1990): 216–25. http://dx.doi.org/10.1162/neco.1990.2.2.216.
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The feasibility of developing a neural network to perform nonlinear Bayesian estimation from sparse data is explored using an example from clinical pharmacology. The problem involves estimating parameters of a dynamic model describing the pharmacokinetics of the bronchodilator theophylline from limited plasma concentration measurements of the drug obtained in a patient. The estimation performance of a backpropagation trained network is compared to that of the maximum likelihood estimator as well as the maximum a posteriori probability estimator. In the example considered, the estimator prediction errors (model parameters and outputs) obtained from the trained neural network were similar to those obtained using the nonlinear Bayesian estimator.
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Ekung, Samuel, Adeniran Lashinde und Emmanuel Adu. „Critical Risks to Construction Cost Estimation“. Journal of Engineering, Project, and Production Management 11, Nr. 1 (01.01.2021): 19–29. http://dx.doi.org/10.2478/jeppm-2021-0003.
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AbstractThe prevalence of cost overrun in project delivery suggests an acute dearth of inclusive understanding of the effect of risks on construction cost estimation. In aberrant to the generic assumptions, customary to inquiries in construction risk researches, this paper appraised critical construction estimating risks. The study evaluated the sources, frequency and significance of construction estimating risks, using data from a questionnaire survey of 206 quantity surveyors in Nigeria. The data were analysed using factor analysis, Fussy Set Theory, Terrell Transformation Index (TTI), and Kruskal Wallis H tests. The results showed that estimating risks are correlate seven principal sources, namely: estimating resources, construction knowledge, design information, economic condition, the expertise of estimator, geographic factor, cost data, and project factors (λ, > 0.70 <1.0). Twenty-nine risk factors likewise emerged critical construction estimation risks (TTI, 69-87 > 65 percent) and the top three were low construction knowledge, inaccurate cost information and changes in government regulations (factor scores > 0.60 > 0.50). The awareness and accurate assessment of these risks into project cost estimation would reduce cost overrun. The study, therefore, recommends synergies between projects’ internal/ external environments for proper scoping of these risks into project estimates.
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Venturino, Antonello, Cristina Stoica Maniu, Sylvain Bertrand, Teodoro Alamo und Eduardo F. Camacho. „Distributed moving horizon state estimation for sensor networks with low computation capabilities“. SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL 1, Nr. 1 (30.06.2021): 81–87. http://dx.doi.org/10.52846/stccj.2021.1.1.14.
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This paper focuses on distributed state estimation for sensor network observing a discrete-time linear system. The provided solution is based on a Distributed Moving Horizon Estimation (DMHE) algorithm considering a pre-estimating Luenberger observer in the formulation of the local problem solved by each sensor. This leads to reduce the computation load, while preserving the accuracy of the estimation. Moreover, observability properties of local sensors are used for tuning the weights related to consensus information fusion built on a rank-based condition, in order to improve the convergence of the estimation error. Results obtained by Monte Carlo simulations are provided to compare the performance with existing approaches, in terms of accuracy of the estimations and computation time.
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Zhang, Ren-Qian, Qi-Qi Wang, Yi-Ye Zhang, Hai-Tao Zheng und Jie Hu. „Estimation of Jointly Normally Distributed Demand for Cross-Selling Items in Inventory Systems with Lost Sales“. Mathematical Problems in Engineering 2019 (16.07.2019): 1–21. http://dx.doi.org/10.1155/2019/7219326.
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Demand estimation is often confronted with incomplete information of censored demand because of lost sales. Many estimators have been proposed to deal with lost sales when estimating the parameters of demand distribution. This study introduces the cross-selling effect into estimations, where two items are cross-sold because of the positive externality in a newsvendor-type inventory system. We propose an approach to estimate the parameters of a jointly normally distributed demand for two cross-selling items based on an iterative framework considering lost sales. Computational results based on more than two million numerical examples show that our estimator achieves high precision. Compared with the point estimations without lost sales, all the relative errors of the estimations of demand expectation, standard deviation, and correlation coefficient are no larger than 2% on average if the sample size is no smaller than 800. In particular, for demand expectation, the error is smaller than 1% if the comprehensive censoring level is no larger than four standard deviations (implying a 2σ-level of safety stock for each item), even if the sample size decreases to 50. This implies that the demand estimator should be competent in modern inventory systems that are rich in data.
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Gao, Jing, Kehan Bai und Wenhao Gui. „Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring“. Symmetry 12, Nr. 5 (05.05.2020): 731. http://dx.doi.org/10.3390/sym12050731.
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Two estimation problems are studied based on the general progressively censored samples, and the distributions from the inverted scale family (ISF) are considered as prospective life distributions. One is the exact interval estimation for the unknown parameter θ , which is achieved by constructing the pivotal quantity. Through Monte Carlo simulations, the average 90 % and 95 % confidence intervals are obtained, and the validity of the above interval estimation is illustrated with a numerical example. The other is the estimation of R = P ( Y < X ) in the case of ISF. The maximum likelihood estimator (MLE) as well as approximate maximum likelihood estimator (AMLE) is obtained, together with the corresponding R-symmetric asymptotic confidence intervals. With Bootstrap methods, we also propose two R-asymmetric confidence intervals, which have a good performance for small samples. Furthermore, assuming the scale parameters follow independent gamma priors, the Bayesian estimator as well as the HPD credible interval of R is thus acquired. Finally, we make an evaluation on the effectiveness of the proposed estimations through Monte Carlo simulations and provide an illustrative example of two real datasets.
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Mohd Shariff, Khairul Khaizi, Suraya Zainuddin, Noor Hafizah Abdul Aziz, Nur Emileen Abd Rashid und Nor Ayu Zalina Zakaria. „Spectral estimator effects on accuracy of speed-over-ground radar“. International Journal of Electrical and Computer Engineering (IJECE) 12, Nr. 4 (01.08.2022): 3900. http://dx.doi.org/10.11591/ijece.v12i4.pp3900-3910.
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<p>Spectral estimation is a critical signal processing step in speed-over-ground (SoG) radar. It is argued that, for accurate speed estimation, spectral estimation should use low bias and variance estimator. However, there is no evaluation on spectral estimation techniques in terms of estimating mean Doppler frequency to date. In this paper, we evaluate two common spectral estimation techniques, namely periodogram based on Fourier transformation and the autoregressive (AR) based on burg algorithm. These spectral estimators are evaluated in terms of their bias and variance in estimating a mean frequency. For this purpose, the spectral estimators are evaluated with different Doppler signals that varied in mean frequency and signal-to-noise ratio (SNR). Results in this study indicates that the periodogram method performs well in most of the tests while the AR method did not perform as well as these but offered a slight improvement over the periodogram in terms of variance.</p>
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Fredlund, Delwyn G., Daichao Sheng und Jidong Zhao. „Estimation of soil suction from the soil-water characteristic curve“. Canadian Geotechnical Journal 48, Nr. 2 (Februar 2011): 186–98. http://dx.doi.org/10.1139/t10-060.
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Soil-water characteristic curves (SWCCs) are routinely used for the estimation of unsaturated soil property functions (e.g., permeability functions, water storage functions, shear strength functions, and thermal property functions). This paper examines the possibility of using the SWCC for the estimation of in situ soil suction. The paper focuses on the limitations of estimating soil suctions from the SWCC and also suggests a context under which soil suction estimations should be used. The potential range of estimated suction values is known to be large because of hysteresis between drying and wetting SWCCs. For this, and other reasons, the estimation of in situ suctions from the SWCC has been discouraged. However, a framework is suggested in this paper for estimating the median value for in situ soil suction along with a likely range of soil suction values (i.e., maximum and minimum values). The percentage error in the estimation of soil suction from the SWCC is shown to be lowest for sand soils and highest for clay soils.
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Jung, J., J. Lee und K. Huh. „Robust contact force estimation for robot manipulators in three-dimensional space“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, Nr. 9 (01.09.2006): 1317–27. http://dx.doi.org/10.1243/09544062c09005.
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Information on contact forces in robot manipulators is indispensable for fast and accurate force control. Instead of expensive force sensors, estimation algorithms for contact forces have been widely developed. However, it is not easy to obtain the accurate values due to uncertainties. In this article, a new robust estimator is proposed to estimate three-dimensional contact forces acting on a three-link robot manipulator. The estimator is based on the extended Kalman filter (EKF) structure combined with a Lyapunov-based adaptation law for estimating the contact force. In contrast to the conventional EKF the new estimator is designed such that it is robust to the deterministic uncertainties such as the modelling error and the sensing bias. The performance of the proposed estimator is evaluated through simulations of a robot manipulator and demonstrates robustness in estimating the contact force. The estimation results show that it can be potentially used to replace the expensive force sensors in robot applications.
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Huang, Du Jou, Yu Ju Chen, Huang Chu Huang, Yu An Lin und Rey Chue Hwang. „The TP Chromatic Aberration Estimation by Using Neural Networks“. Applied Mechanics and Materials 121-126 (Oktober 2011): 4239–43. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.4239.
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The chromatic aberration estimations of touch panel (TP) film by using neural networks are presented in this paper. The neural networks with error back-propagation (BP) learning algorithm were used to catch the complex relationship between the chromatic aberration, i.e., L.A.B. values, and the relative parameters of TP decoration film. An artificial intelligent (AI) estimator based on neural model for the estimation of physical property of TP film is expected to be developed. From the simulation results shown, the estimations of chromatic aberration of TP film are very accurate. In other words, such an AI estimator is quite promising and potential in commercial using.
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Guure, Chris Bambey, Noor Akma Ibrahim und Al Omari Mohammed Ahmed. „Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys' Prior Information with Three Loss Functions“. Mathematical Problems in Engineering 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/589640.
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The Weibull distribution has been observed as one of the most useful distribution, for modelling and analysing lifetime data in engineering, biology, and others. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameters estimation which is in contention with other estimation methods. In this paper, we examine the performance of maximum likelihood estimator and Bayesian estimator using extension of Jeffreys prior information with three loss functions, namely, the linear exponential loss, general entropy loss, and the square error loss function for estimating the two-parameter Weibull failure time distribution. These methods are compared using mean square error through simulation study with varying sample sizes. The results show that Bayesian estimator using extension of Jeffreys' prior under linear exponential loss function in most cases gives the smallest mean square error and absolute bias for both the scale parameterαand the shape parameterβfor the given values of extension of Jeffreys' prior.
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Chen, Zhenmin, und Feng Miao. „Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution“. International Journal of Quality, Statistics, and Reliability 2012 (08.08.2012): 1–6. http://dx.doi.org/10.1155/2012/897106.
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The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation result shows that the proposed method is less biased in estimating the location parameter. The large sample size case is discussed in the paper.
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Abdul Jalil, Nur Raihan, Nur Anisah Mohamed und Rossita Mohamad Yunus. „Estimation in regret-regression using quadratic inference functions with ridge estimator“. PLOS ONE 17, Nr. 7 (21.07.2022): e0271542. http://dx.doi.org/10.1371/journal.pone.0271542.
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In this paper, we propose a new estimation method in estimating optimal dynamic treatment regimes. The quadratic inference functions in myopic regret-regression (QIF-MRr) can be used to estimate the parameters of the mean response at each visit, conditional on previous states and actions. Singularity issues may arise during computation when estimating the parameters in ODTR using QIF-MRr due to multicollinearity. Hence, the ridge penalty was introduced in rQIF-MRr to tackle the issues. A simulation study and an application to anticoagulation dataset were conducted to investigate the model’s performance in parameter estimation. The results show that estimations using rQIF-MRr are more efficient than the QIF-MRr.
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Quan, Zhi, Yingying Zhang, Jie Liu und Yao Wang. „Maximum Element Dichotomous Coordinate Descent Based Minimum Variance Distortionless Response DoA Estimator“. Electronics 10, Nr. 23 (28.11.2021): 2966. http://dx.doi.org/10.3390/electronics10232966.
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In this paper, we devise an efficient approach for estimating the direction of arrival (DoA). The proposed DoA estimation approach is based on minimum variance distortionless response (MVDR) criteria within a recursive least squares (RLS) framework. The dichotomous coordinate descent algorithm is used to modify the calculation of the output power spectrum, and a diagonal loading term is applied to improve the robustness of the DoA estimator. These modifications allow us to both reduce the computational complexity of the RLS DoA estimator and increase the estimation performance. A numerical comparison confirms that the proposed DoA estimator outperforms the conventional RLS DoA estimator in terms of the computational complexity and DoA estimation error. Finally, the proposed theoretical DoA estimator is implemented on a field-programmable gate array (FPGA) board to verify the feasibility of the method. The numerical results of a fixed-point implementation demonstrate that the performance of the proposed method is very close to that of its floating-point counterpart.
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Qi, Gengxin, Xiaobin Fan und Hao Li. „A comparative study of the unscented Kalman filter and particle filter estimation methods for the measurement of the road adhesion coefficient“. Mechanical Sciences 13, Nr. 2 (25.08.2022): 735–49. http://dx.doi.org/10.5194/ms-13-735-2022.
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Abstract. The measurement of the road adhesion coefficient is of great significance for the vehicle active safety control system and is one of the key technologies for future autonomous driving. With a focus on the problems of interference uncertainty and system nonlinearity in the estimation of the road adhesion coefficient, this work adopts a vehicle model with 7 degrees of freedom (7-DOF) and the Dugoff tire model and uses these models to estimate the road adhesion coefficient in real time based on the particle filter (PF) algorithm. The estimations using the PF algorithm are verified by selecting typical working conditions, and they are compared with estimations using the unscented Kalman filter (UKF) algorithm. Simulation results show that the road adhesion coefficient estimator error based on the UKF algorithm is less than 7 %, whereas the road adhesion coefficient estimator error based on the PF algorithm is less than 0.1 %. Thus, compared with the UKF algorithm, the PF algorithm has a higher accuracy and control effect with respect to estimating the road adhesion coefficient under different road conditions. In order to verify the robustness of the road adhesion coefficient estimator, an automobile test platform based on a four-wheel-hub-motor car is built. According to the experimental results, the estimator based on the PF algorithm can realize the road surface identification with an error of less than 1 %, which verifies the feasibility and effectiveness of the algorithm with respect to estimating the road adhesion coefficient and shows good robustness.
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ÇINAR, Feyza, und Abdullah Çağrı BIBER. „The relationship between students' computational estimation skills and mathematical self-efficiency“. Acta Didactica Napocensia 17, Nr. 1 (07.09.2024): 84–97. http://dx.doi.org/10.24193/adn.17.1.7.
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The factors related to estimating skills are twofold: cognitive and affective perspectives. Perception of self-efficacy in mathematics, one of the affective factors, is essential for the individual's capacity, abilities, and self-belief in mathematics for the mathematics course. The present study examined the relationship between students' computational estimation skills and mathematical self-efficacy perceptions. For this purpose, two sets of instruments were used as data collection tools: a computational estimation skills task and a mathematical self-efficacy perceptions scale. A correlational design was used in this study, and a total of 83 eighth-grade students participated in the research. As a result, it was concluded that there was a moderately positive and statistically significant relationship between computational estimation skills and mathematical self-efficacy perceptions. Students experience more stress when making estimations compared to mathematical computations whose results are specific. In addition, students mostly need to correct their estimations in questions related to computations with fractions, and they mostly use the rounding strategy when making estimations. These results are further discussed in relation to the perspective of supporting children’s abilities for estimations at the primary school.
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Hirose, Kei, und Hiroki Masuda. „Robust Relative Error Estimation“. Entropy 20, Nr. 9 (24.08.2018): 632. http://dx.doi.org/10.3390/e20090632.
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Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the γ -likelihood function, which is constructed through γ -cross entropy with keeping the original statistical model in use. The estimating equation has a redescending property, a desirable property in robust statistics, for a broad class of noise distributions. To find a minimizer of the negative γ -likelihood function, a majorize-minimization (MM) algorithm is constructed. The proposed algorithm is guaranteed to decrease the negative γ -likelihood function at each iteration. We also derive asymptotic normality of the corresponding estimator together with a simple consistent estimator of the asymptotic covariance matrix, so that we can readily construct approximate confidence sets. Monte Carlo simulation is conducted to investigate the effectiveness of the proposed procedure. Real data analysis illustrates the usefulness of our proposed procedure.
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Kareem, Urdak, und Fadhaa Hashim. „The Use Of Genetic Algorithm In Estimating The Parameter Of Finite Mixture Of Linear Regression“. Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ), Nr. 1 (29.06.2022): 237–52. http://dx.doi.org/10.55562/jrucs.v51i1.536.
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The estimation of the parameters of linear regression is based on the usual Least Square method, as this method is based on the estimation of several basic assumptions. Therefore, the accuracy of estimating the parameters of the model depends on the validity of these hypotheses. The most successful technique was the robust estimation method which is minimizing maximum likelihood estimator (MM-estimator) that proved its efficiency in this purpose. However, the use of the model becomes unrealistic and one of these assumptions is the uniformity of the variance and the normal distribution of the error. These assumptions are not achievable in the case of studying a specific problem that may include complex data of more than one model. To deal with this type of problem, a mixture of linear regression is used to model such data. In this article, we propose a genetic algorithm-based method combined with (MM-estimator), which is called in this article (RobGA), to improve the accuracy of the estimation in the final stage. We compare the suggested method with robust bi-square (MixBi) in terms of their application to real data representing blood sample. The results showed that RobGA is more efficient in estimating the parameters of the model than the MixBi method with respect to mean square error (MSE) and classification error (CE).
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Chen, Liqiong, Antonio F. Galvao und Suyong Song. „Quantile Regression with Generated Regressors“. Econometrics 9, Nr. 2 (12.04.2021): 16. http://dx.doi.org/10.3390/econometrics9020016.
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This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step estimation procedure, where the generated regressors are computed in the first step. The asymptotic properties of the two-step estimator, namely, consistency and asymptotic normality are established. We show that the asymptotic variance-covariance matrix needs to be adjusted to account for the first-step estimation error. We propose a general estimator for the asymptotic variance-covariance, establish its consistency, and develop testing procedures for linear hypotheses in these models. Monte Carlo simulations to evaluate the finite-sample performance of the estimation and inference procedures are provided. Finally, we apply the proposed methods to study Engel curves for various commodities using data from the UK Family Expenditure Survey. We document strong heterogeneity in the estimated Engel curves along the conditional distribution of the budget share of each commodity. The empirical application also emphasizes that correctly estimating confidence intervals for the estimated Engel curves by the proposed estimator is of importance for inference.
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Elie, Romuald. „Double Kernel Estimation of Sensitivities“. Journal of Applied Probability 46, Nr. 3 (September 2009): 791–811. http://dx.doi.org/10.1239/jap/1253279852.
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In this paper we address the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance, for example, the sensitivities of the price of a contingent claim are called the Greeks. A new way of estimating the Greeks has recently been introduced in Elie, Fermanian and Touzi (2007) through a randomization of the parameter of interest combined with nonparametric estimation techniques. In this paper we study another type of estimator that turns out to be closely related to the score function, which is well known to be the optimal Greek weight. This estimator relies on the use of two distinct kernel functions and the main interest of this paper is to provide its asymptotic properties. Under a slightly more stringent condition, its rate of convergence is the same as the one of the estimator introduced in Elie, Fermanian and Touzi (2007) and outperforms the finite differences estimator. In addition to the technical interest of the proofs, this result is very encouraging in the dynamic of creating new types of estimator for the sensitivities.
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Elie, Romuald. „Double Kernel Estimation of Sensitivities“. Journal of Applied Probability 46, Nr. 03 (September 2009): 791–811. http://dx.doi.org/10.1017/s002190020000588x.
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In this paper we address the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance, for example, the sensitivities of the price of a contingent claim are called the Greeks. A new way of estimating the Greeks has recently been introduced in Elie, Fermanian and Touzi (2007) through a randomization of the parameter of interest combined with nonparametric estimation techniques. In this paper we study another type of estimator that turns out to be closely related to the score function, which is well known to be the optimal Greek weight. This estimator relies on the use of two distinct kernel functions and the main interest of this paper is to provide its asymptotic properties. Under a slightly more stringent condition, its rate of convergence is the same as the one of the estimator introduced in Elie, Fermanian and Touzi (2007) and outperforms the finite differences estimator. In addition to the technical interest of the proofs, this result is very encouraging in the dynamic of creating new types of estimator for the sensitivities.
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Gillard, Nicolas, Étienne Belin und François Chapeau-Blondeau. „Stochastic Resonance with Unital Quantum Noise“. Fluctuation and Noise Letters 18, Nr. 03 (16.07.2019): 1950015. http://dx.doi.org/10.1142/s0219477519500159.
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The fundamental quantum information processing task of estimating the phase of a qubit is considered. Following quantum measurement, the estimation efficiency is evaluated by the classical Fisher information which determines the best performance limiting any estimator and achievable by the maximum likelihood estimator. The estimation process is analyzed in the presence of decoherence represented by essential quantum noises that can affect the qubit and belonging to the broad class of unital quantum noises. Such a class especially contains the bit-flip, the phase-flip, the depolarizing noises, or the whole family of Pauli noises. As the level of noise is increased, we report the possibility of non-standard behaviors where the estimation efficiency does not necessarily deteriorate uniformly, but can experience non-monotonic variations. Regimes are found where higher noise levels prove more favorable to estimation. Such behaviors are related to stochastic resonance effects in signal estimation, shown here feasible for the first time with unital quantum noises. The results provide enhanced appreciation of quantum noise or decoherence, manifesting that it is not always detrimental for quantum information processing.