Journal articles: 'Estimation theory'

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Odoh, Dr Mcchester, and Dr Ihedigbo Chinedum E. "Estimation Theory." IOSR Journal of Computer Engineering 16, no. 6 (2014): 30–35. http://dx.doi.org/10.9790/0661-16623035.

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Saikkonen, Pentti. "Asymptotically Efficient Estimation of Cointegration Regressions." Econometric Theory 7, no. 1 (March 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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Altounji, Nizar, Mohamed Bisher Zeina, and Moustafa Mazhar Ranneh. "Introduction to Neutrosophic Bayes Estimation Theory." Galoitica: Journal of Mathematical Structures and Applications 7, no. 1 (2023): 43–50. http://dx.doi.org/10.54216/gjmsa.070105.

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This research presents the concept of neutrosophic Bayesian estimation defining the neutrosophic loss function, neutrosophic risk function, neutrosophic posterior risk function and neutrosophic maximum a posteriori estimator. Minimization of the neutrosophic posterior risk of the estimator is also discussed. An algebraic isomorphism is used to simplify equations solving. As an application of the presented theorems, a sample drawn from a neutrosophic gamma distribution with a conjugate prior is discussed and studied and the parameter of the formulated distribution is successfully estimated using neutrosophic quadratic loss function which results an estimator that equals the posterior mean.

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Rodríguez-García, Marco A., Isaac Pérez Castillo, and P. Barberis-Blostein. "Efficient qubit phase estimation using adaptive measurements." Quantum 5 (June 4, 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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Ghlib, Imane, Youcef Messlem, and Zakaria Chedjara. "An Improved Sensorless Control of Induction Motor Using ADALINE: Theory and Experiment." Journal Européen des Systèmes Automatisés 55, no. 2 (April 30, 2022): 221–27. http://dx.doi.org/10.18280/jesa.550209.

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This article develops a new observer to achieve highly speed estimation for induction motor control. Its principle consists of estimating flux and speed separately, by using linear Luenberger as flux observer and intelligent PI controller as rotor speed estimator. Considering that is generally challenging to established proper PI parameters, the ADALINE algorithm is integrated as a trainable module to automatically calculate the KP and the KI gains in each iteration during all operation induction motor. This algorithm helps to search on the one hand the best regulation of the controller in real-time, taking into account the objectives to achieve (an accurate estimation) and the respect constraints (heavy calculation). On the other hand, it makes it possible to improve the adaptive Luenberger estimation problem in the unobservable zone (low speed). The experimental comparison of the observers demonstrates the visible improvement of the enhanced observer. It can converge to real speed in a short time with less static and transient error.

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Xu, Ke-Li. "REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS." Econometric Theory 26, no. 2 (September 30, 2009): 541–63. http://dx.doi.org/10.1017/s0266466609100087.

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The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

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Chan, Hock Peng, Chiang-Wee Heng, and Ajay Jasra. "Theory of segmented particle filters." Advances in Applied Probability 48, no. 1 (March 2016): 69–87. http://dx.doi.org/10.1017/apr.2015.7.

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AbstractWe study the asymptotic behavior of a new particle filter approach for the estimation of hidden Markov models. In particular, we develop an algorithm where the latent-state sequence is segmented into multiple shorter portions, with an estimation technique based upon a separate particle filter in each portion. The partitioning facilitates the use of parallel processing, which reduces the wall-clock computational time. Based upon this approach, we introduce new estimators of the latent states and likelihood which have similar or better variance properties compared to estimators derived from standard particle filters. We show that the likelihood function estimator is unbiased, and show asymptotic normality of the underlying estimators.

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Zieliński, Ryszard. "Theory of parameter estimation." Banach Center Publications 41, no. 2 (1997): 209–20. http://dx.doi.org/10.4064/-41-2-209-220.

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Ziegel, Eric R., E. L. Lehmann, and George Casella. "Theory of Point Estimation." Technometrics 41, no. 3 (August 1999): 274. http://dx.doi.org/10.2307/1270597.

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Strawderman, William E., E. L. Lehmann, and George Casella. "Theory of Point Estimation." Journal of the American Statistical Association 95, no. 449 (March 2000): 329. http://dx.doi.org/10.2307/2669560.

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11

Waal, D. J. de, P. C. N. Groenewald, J. M. van Zyl, and J. V. Zidek. "MULTI-ΒAYESIAN ESTIMATION THEORY." Statistics & Risk Modeling 4, no. 1 (January 1986): 1–18. http://dx.doi.org/10.1524/strm.1986.4.1.1.

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Ramm, A. G. "Random fields estimation theory." Mathematical and Computer Modelling 13, no. 4 (1990): 87–100. http://dx.doi.org/10.1016/0895-7177(90)90056-s.

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13

Ekung, Samuel, Adeniran Lashinde, and Emmanuel Adu. "Critical Risks to Construction Cost Estimation." Journal of Engineering, Project, and Production Management 11, no. 1 (January 1, 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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Hotta, L. K., E. C. Lucas, and H. P. Palaro. "Estimation of VaR Using Copula and Extreme Value Theory." Multinational Finance Journal 12, no. 3/4 (December 1, 2008): 205–18. http://dx.doi.org/10.17578/12-3/4-3.

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15

Henriques-Rodrigues, Lígia, and M. Ivette Gomes. "Box-Cox Transformations and Bias Reduction in Extreme Value Theory." Computational and Mathematical Methods 2022 (March 10, 2022): 1–15. http://dx.doi.org/10.1155/2022/3854763.

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The Box-Cox transformations are used to make the data more suitable for statistical analysis. We know from the literature that this transformation of the data can increase the rate of convergence of the tail of the distribution to the generalized extreme value distribution, and as a byproduct, the bias of the estimation procedure is reduced. The reduction of bias of the Hill estimator has been widely addressed in the literature of extreme value theory. Several techniques have been used to achieve such reduction of bias, either by removing the main component of the bias of the Hill estimator of the extreme value index (EVI) or by constructing new estimators based on generalized means or norms that generalize the Hill estimator. We are going to study the Box-Cox Hill estimator introduced by Teugels and Vanroelen, in 2004, proving the consistency and asymptotic normality of the estimator and addressing the choice and estimation of the power and shift parameters of the Box-Cox transformation for the EVI estimation. The performance of the estimators under study will be illustrated for finite samples through small-scale Monte Carlo simulation studies.

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Kaji, Tetsuya. "Theory of Weak Identification in Semiparametric Models." Econometrica 89, no. 2 (2021): 733–63. http://dx.doi.org/10.3982/ecta16413.

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We provide general formulation of weak identification in semiparametric models and an efficiency concept. Weak identification occurs when a parameter is weakly regular, that is, when it is locally homogeneous of degree zero. When this happens, consistent or equivariant estimation is shown to be impossible. We then show that there exists an underlying regular parameter that fully characterizes the weakly regular parameter. While this parameter is not unique, concepts of sufficiency and minimality help pin down a desirable one. If estimation of minimal sufficient underlying parameters is inefficient, it introduces noise in the corresponding estimation of weakly regular parameters, whence we can improve the estimators by local asymptotic Rao–Blackwellization. We call an estimator weakly efficient if it does not admit such improvement. New weakly efficient estimators are presented in linear IV and nonlinear regression models. Simulation of a linear IV model demonstrates how 2SLS and optimal IV estimators are improved.

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Breunig, Christoph, and Jan Johannes. "ADAPTIVE ESTIMATION OF FUNCTIONALS IN NONPARAMETRIC INSTRUMENTAL REGRESSION." Econometric Theory 32, no. 3 (March 30, 2015): 612–54. http://dx.doi.org/10.1017/s0266466614000966.

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We consider the problem of estimating the valueℓ(ϕ) of a linear functional, where the structural functionϕmodels a nonparametric relationship in presence of instrumental variables. We propose a plug-in estimator which is based on a dimension reduction technique and additional thresholding. It is shown that this estimator is consistent and can attain the minimax optimal rate of convergence under additional regularity conditions. This, however, requires an optimal choice of the dimension parametermdepending on certain characteristics of the structural functionϕand the joint distribution of the regressor and the instrument, which are unknown in practice. We propose a fully data driven choice ofmwhich combines model selection and Lepski’s method. We show that the adaptive estimator attains the optimal rate of convergence up to a logarithmic factor. The theory in this paper is illustrated by considering classical smoothness assumptions and we discuss examples such as pointwise estimation or estimation of averages of the structural functionϕ.

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Marengo, Edwin A. "Multipole Theory and Algorithms for Target Support Estimation." International Journal of Antennas and Propagation 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/515240.

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The inverse problem of estimating the smallest region of localization (minimum source region) of a source or scatterer that can produce a given radiation or scattered field is investigated with the help of the multipole expansion. The results are derived in the framework of the scalar Helmholtz equation. The proposed approach allows the estimation of possibly nonconvex minimum source regions. The derived method is illustrated with an example relevant to inverse scattering.

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Zhu, Jun Tao, Chang Yu Sun, and Yuan Yuan Jiao. "Estimation Based on Expectation Theory." Applied Mechanics and Materials 204-208 (October 2012): 4868–71. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4868.

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The theory of expectation estimation is put forward to discuss the estimation quality of the expectation domain. It is demonstrated that the “validity” criterion of the estimation theory in mathematical statistics (named classic estimate later) isn’t right and arithmetical average value x isn’t the best estimate. The means of characteristic value estimate (N (0, 1) estimate) is suggested to demonstrate the expectation estimate domain.

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Domènech Massons, José M. "Fundamentals of Decision Theory and Statistical Estimation Theory." Quaderns de Psicologia, no. 1 (September 11, 2009): 50. http://dx.doi.org/10.5565/rev/qpsicologia.320.

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Xiao, Ming Zhu. "Estimating Measurement Error Based on Evidence Theory." Advanced Materials Research 548 (July 2012): 839–42. http://dx.doi.org/10.4028/www.scientific.net/amr.548.839.

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Measurement error is traditionally represented with probability distributions. Although probabilistic representations of measurement error have been successfully employed in many analyses, such representations have been criticized for requiring more refined knowledge with respect to the existing error than that is really present. As a result, this paper proposes a general framework and process for estimating the measurement error based on evidence theory. In this research cumulative belief functions (CBFs) and cumulative plausibility functions (CPFs) are used to estimate measurement error. The estimation includes two steps:(1) modeling the parameters by means of a random set, and discrediting the random set to focal elements in finite numbers; (2)summarizing the propagation error. An example is demonstrated the estimation process.

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Contreras-Reyes, Javier E. "Information–Theoretic Aspects of Location Parameter Estimation under Skew–Normal Settings." Entropy 24, no. 3 (March 13, 2022): 399. http://dx.doi.org/10.3390/e24030399.

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In several applications, the assumption of normality is often violated in data with some level of skewness, so skewness affects the mean’s estimation. The class of skew–normal distributions is considered, given their flexibility for modeling data with asymmetry parameter. In this paper, we considered two location parameter (μ) estimation methods in the skew–normal setting, where the coefficient of variation and the skewness parameter are known. Specifically, the least square estimator (LSE) and the best unbiased estimator (BUE) for μ are considered. The properties for BUE (which dominates LSE) using classic theorems of information theory are explored, which provides a way to measure the uncertainty of location parameter estimations. Specifically, inequalities based on convexity property enable obtaining lower and upper bounds for differential entropy and Fisher information. Some simulations illustrate the behavior of differential entropy and Fisher information bounds.

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HARA, Shinsuke. "Statistical Estimation Theory in Localization." IEICE ESS FUNDAMENTALS REVIEW 4, no. 1 (2010): 32–38. http://dx.doi.org/10.1587/essfr.4.32.

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DePriest, Douglas J. "Lessons in Digital Estimation Theory." Technometrics 30, no. 1 (February 1988): 128–29. http://dx.doi.org/10.1080/00401706.1988.10488349.

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Giannakis, Georgios B. "Lessons in digital estimation theory." Automatica 26, no. 1 (January 1990): 187–88. http://dx.doi.org/10.1016/0005-1098(90)90172-e.

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Rohling, H. "Lessons in digital estimation theory." Signal Processing 16, no. 2 (February 1989): 183. http://dx.doi.org/10.1016/0165-1684(89)90099-6.

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Gu, Chong, and Chunfu Qiu. "Smoothing Spline Density Estimation: Theory." Annals of Statistics 21, no. 1 (March 1993): 217–34. http://dx.doi.org/10.1214/aos/1176349023.

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Spokoiny, Vladimir. "Parametric estimation. Finite sample theory." Annals of Statistics 40, no. 6 (December 2012): 2877–909. http://dx.doi.org/10.1214/12-aos1054.

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Girko, Vyacheslav L. "Spectral theory of minimax estimation." Acta Applicandae Mathematicae 43, no. 1 (April 1996): 59–69. http://dx.doi.org/10.1007/bf00046987.

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SUZUKI, Katsuo, Junya SHIMAZAKI, and Yoshikuni SHINOHARA. "Estimation of Net Reactivity Based on H.INF. Estimation Theory." Journal of the Atomic Energy Society of Japan / Atomic Energy Society of Japan 36, no. 1 (1994): 79–88. http://dx.doi.org/10.3327/jaesj.36.79.

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Muela, Sonia Benito, Carmen López-Martín, and Mª Ángeles Navarro. "The Role of the Skewed Distributions in the Framework of Extreme Value Theory (EVT)." International Business Research 10, no. 11 (October 13, 2017): 88. http://dx.doi.org/10.5539/ibr.v10n11p88.

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In this paper, we analyze the role of the heavy tail and skewed distribution in market risk estimation (Value at Risk (VaR)). In particular, we are interested in knowing if in the framework of the conditional extreme value theory, the estimation of the volatility model below heavy tail and skewed distribution contributes to improve the VaR estimation respect to these obtained from a symmetric distribution. The study has been carried out for six individual assets belonging to the digital sector: ADP, Amazon, Cerner, Apple, Microsoft and Telefonica. The analysis period runs from January 1st, 2008 to the end of December 2013. Although the evidence found is a little bit weak, the results obtained seem to indicate that the heavy tail and skewed distribution outperforms the symmetric distribution both in terms of accuracy VaR estimations as in terms of firm’s loss function. Furthermore, the market risk capital requirements fixed on the base of the VaR estimations are also lowest below a skewed distribution.

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Marchese, Marta Maria, Alessio Belenchia, and Mauro Paternostro. "Optomechanics-Based Quantum Estimation Theory for Collapse Models." Entropy 25, no. 3 (March 14, 2023): 500. http://dx.doi.org/10.3390/e25030500.

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We make use of the powerful formalism of quantum parameter estimation to assess the characteristic rates of a continuous spontaneous localization (CSL) model affecting the motion of a massive mechanical system. We show that a study performed in non-equilibrium conditions unveils the advantages provided by the use of genuinely quantum resources—such as quantum correlations—in estimating the CSL-induced diffusion rate. In stationary conditions, instead, the gap between quantum performance and a classical scheme disappears. Our investigation contributes to the ongoing effort aimed at identifying suitable conditions for the experimental assessment of collapse models.

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Jin, Hanqing, and Shige Peng. "Optimal unbiased estimation for maximal distribution." Probability, Uncertainty and Quantitative Risk 6, no. 3 (2021): 189. http://dx.doi.org/10.3934/puqr.2021009.

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<p style='text-indent:20px;'>Unbiased estimation for parameters of maximal distribution is a fundamental problem in the statistical theory of sublinear expectations. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper mean and the minimum estimator is the smallest unbiased estimator for the lower mean.</p>

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Alexei, Kaltchenko. "Estimation of quantum entropies." i-manager’s Journal on Mathematics 13, no. 1 (2024): 1. http://dx.doi.org/10.26634/jmat.13.1.20387.

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Motivated by the importance of entropy functions in quantum data compression, entanglement theory, and various quantum information-processing tasks, this study demonstrates how classical algorithms for entropy estimation can effectively contribute to the construction of quantum algorithms for universal quantum entropy estimation. Given two quantum i.i.d. sources with completely unknown density matrices, algorithms are developed for estimating quantum cross entropy and quantum relative entropy. These estimation techniques represent a quantum generalization of the classical algorithms by Lempel, Ziv, and Merhav.

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Lee, Sang-Won, and Bruce E. Hansen. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator." Econometric Theory 10, no. 1 (March 1994): 29–52. http://dx.doi.org/10.1017/s0266466600008215.

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This paper investigates the sampling behavior of the quasi-maximum likelihood estimator of the Gaussian GARCH(1,1) model. The rescaled variable (the ratio of the disturbance to the conditional standard deviation) is not required to be Gaussian nor independent over time, in contrast to the current literature. The GARCH process may be integrated (α + β = 1), or even mildly explosive (α + β > 1). A bounded conditional fourth moment of the rescaled variable is sufficient for the results. Consistent estimation and asymptotic normality are demonstrated, as well as consistent estimation of the asymptotic covariance matrix.

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Tian, Cheng, Bo Leng, Xinchen Hou, Lu Xiong, and Chao Huang. "Multi-Sensor Fusion Based Estimation of Tire-Road Peak Adhesion Coefficient Considering Model Uncertainty." Remote Sensing 14, no. 21 (November 5, 2022): 5583. http://dx.doi.org/10.3390/rs14215583.

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The tire-road peak adhesion coefficient (TRPAC), which cannot be directly measured by on-board sensors, is essential to road traffic safety. Reliable TRPAC estimation can not only serve the vehicle active safety system, but also benefit the safety of other traffic participants. In this paper, a TRPAC fusion estimation method considering model uncertainty is proposed. Based on virtual sensing theory, an image-based fusion estimator considering the uncertainty of the deep-learning model and the kinematic model is designed to realize the accurate classification of the road surface condition on which the vehicle will travel in the future. Then, a dynamics-image-based fusion estimator considering the uncertainty of visual information is proposed based on gain scheduling theory. The results of simulation and real vehicle experiments show that the proposed fusion estimation method can make full use of multisource sensor information, and has significant advantages in estimation accuracy, convergence speed and estimation robustness compared with other single-source-based estimators.

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Moon, Kevin, Kumar Sricharan, Kristjan Greenewald, and Alfred Hero. "Ensemble Estimation of Information Divergence †." Entropy 20, no. 8 (July 27, 2018): 560. http://dx.doi.org/10.3390/e20080560.

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Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the parametric rate when the densities are sufficiently smooth. Guidelines for the tuning parameter selection and the asymptotic distribution of this estimator are provided. Based on the theory, an empirical estimator of Rényi-α divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions. The estimator is shown to be robust to the choice of tuning parameters. We show extensive simulation results that verify the theoretical results of our paper. Finally, we apply the proposed estimator to estimate the bounds on the Bayes error rate of a cell classification problem.

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Klimešová, D., and E. Ocelíková. "Spatial data modelling and maximum entropy theory." Agricultural Economics (Zemědělská ekonomika) 51, No. 2 (February 20, 2012): 80–83. http://dx.doi.org/10.17221/5080-agricecon.

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Spatial data modelling and consequential error estimation of the distribution function are key points of spatial analysis. For many practical problems, it is impossible to hypothesize distribution function firstly and some distribution models, such as Gaussian distribution, may not suit to complicated distribution in practice. The paper shows the possibility of the approach based on the maximum entropy theory that can optimally describe the spatial data distribution and gives  the actual error estimation. 

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Van Deusen, Paul C. "Multiple-Occasion Partial Replacement Sampling for Growth Components." Forest Science 35, no. 2 (June 1, 1989): 388–400. http://dx.doi.org/10.1093/forestscience/35.2.388.

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Abstract The Ware and Cunia (1962) method for estimating volume at time 2 from sampling with partial replacement is proven to be equivalent to a generalized least squares estimator (GLS). The GLS approach is advantageous because it extends easily to encompass multiple occasion sampling with partial replacement (MOSPR). An iterative GLS procedure is given for simultaneously estimating population parameters and their variances that avoids incompatibility problems that arose with some previously published methods. The MOSPR theory is also extended to include growth component estimation with additivity constraints. For. Sci. 35(2):388-400.

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Koike, Yuta. "De-Biased Graphical Lasso for High-Frequency Data." Entropy 22, no. 4 (April 17, 2020): 456. http://dx.doi.org/10.3390/e22040456.

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This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for entries of the precision matrix. To accomplish this purpose, we establish an abstract asymptotic theory for the weighted graphical Lasso and its de-biased version without specifying the form of the initial covariance estimator. We also extend the scope of the theory to the case that a known factor structure is present in the data. The developed theory is applied to the concrete situation where we can use the realized covariance matrix as the initial covariance estimator, and we obtain a feasible asymptotic distribution theory to construct (simultaneous) confidence intervals and (multiple) testing procedures for entries of the precision matrix.

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Ledl, Thomas. "Kernel Density Estimation: Theory and Application in Discriminant Analysis." Austrian Journal of Statistics 33, no. 3 (April 3, 2016): 267–79. http://dx.doi.org/10.17713/ajs.v33i3.441.

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Nowadays, one can find a huge set of methods to estimate the density function of a random variable nonparametrically. Since the first version of the most elementary nonparametric density estimator (the histogram) researchers produced a vast amount of ideas especially corresponding to the issue of choosing the bandwidth parameter in a kernel density estimator model. To focus not only on a descriptive application, the model seems to be quite suitable for application in discriminant analysis, where (multivariate) class densities are the basis for the assignment of a vector to a given class. Thisarticle gives insight to most popular bandwidth parameter selectors as well as to the performance of the kernel density estimator as a classification method compared to the classical linear and quadratic discriminant analysis, respectively. Both a direct estimation in a multivariate space as well as an application of the concept to marginal normalizations of the single variables will be taken into consideration. From this report the gap between theory and application is going to be pointed out.

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Hussain, Attique, Muhammad Shahid Mahmood, Amjad Mahmood, and Ayesha Ashraf. "Median estimation in the presence of non-response using randomised response technique." Natural and Applied Sciences International Journal (NASIJ) 4, no. 2 (December 31, 2023): 108–23. http://dx.doi.org/10.47264/idea.nasij/4.2.7.

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The theory of parameter estimation was developed a long time ago and is currently a widely accepted scientific approach. In some situations where the mean has to deal with the effect of extreme values, the median can be used instead. As there is almost little literature available on median estimation in the existence of non-responsive with the help of the Randomized Response Technique (RRT), the main objective of this paper was to develop a basic theoretical framework for median estimation in the existence of non-responsive with the help of RRT. In this work, we suggested median estimation for delicate variables in auxiliary information using a randomised response model. We have suggested a basic median estimator, product, ratio, exponential product, exponential ratio, and regression cum ratio estimation of the median for non-response by utilising RRT. The mathematical derivations for optimum values of constants, biasness, and Mean Square Error (MSE) of purposed estimators result from the application of well-known Taylor and exponential expansions. The performance of mentioned estimators is evaluated through the numerical study of two populations which discovered the regression cum ratio estimate is more proficient than the remaining estimations mentioned in this article.

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Ao, Ziqiao, and Jinglai Li. "Entropy Estimation via Normalizing Flow." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (June 28, 2022): 9990–98. http://dx.doi.org/10.1609/aaai.v36i9.21237.

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Entropy estimation is an important problem in information theory and statistical science. Many popular entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for high dimensional problems. In this work we propose a transformbased method for high dimensional entropy estimation, which consists of the following two main ingredients. First by modifying the k-NN based entropy estimator, we propose a new estimator which enjoys small estimation bias for samples that are close to a uniform distribution. Second we design a normalizing flow based mapping that pushes samples toward a uniform distribution, and the relation between the entropy of the original samples and the transformed ones is also derived. As a result the entropy of a given set of samples is estimated by first transforming them toward a uniform distribution and then applying the proposed estimator to the transformed samples. Numerical experiments demonstrate the effectiveness of the method for high dimensional entropy estimation problems.

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Ou, Gwo-Bin, and Robert B. Herrmann. "Estimation Theory for Peak Ground Motion." Seismological Research Letters 61, no. 2 (April 1, 1990): 99–107. http://dx.doi.org/10.1785/gssrl.61.2.99.

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Abstract The application of estimation theory for predicting peak ground motion is critically examined in order to be more precise in its application. Estimation theory relates peak ground motion to the duration and spectrum of the signal. Using vertical component data from the Eastern Canada Telemetered Network, at distance range of 100–1000 km, we find that a duration must be defined by the interval where the cumulative energy of the main signal increases linearly, here between 5% and 75% of the cumulative power. This duration, when used with the spectra within this window, adequately replicates observed peak motions. This duration used differs significantly from that used by Herrmann (1985) and Toro and McGuire (1987) beyond 500 km. The estimation theory is extended to estimate confidence limits on the peak motion. Finally, the relation between various spectral level estimators, linear, logarithmic, and RMS, is considered to point out the need for consistency in spectral level estimation using smooth models.

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Song, Yafei, and Xiaodan Wang. "Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/412045.

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Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.

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Vasyura-Bathke, H., J. Dettmer, R. Dutta, P. M. Mai, and S. Jónsson. "Accounting for theory errors with empirical Bayesian noise models in nonlinear centroid moment tensor estimation." Geophysical Journal International 225, no. 2 (January 25, 2021): 1412–31. http://dx.doi.org/10.1093/gji/ggab034.

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SUMMARY Centroid moment tensor (CMT) parameters can be estimated from seismic waveforms. Since these data indirectly observe the deformation process, CMTs are inferred as solutions to inverse problems which are generally underdetermined and require significant assumptions, including assumptions about data noise. Broadly speaking, we consider noise to include both theory and measurement errors, where theory errors are due to assumptions in the inverse problem and measurement errors are caused by the measurement process. While data errors are routinely included in parameter estimation for full CMTs, less attention has been paid to theory errors related to velocity-model uncertainties and how these affect the resulting moment-tensor (MT) uncertainties. Therefore, rigorous uncertainty quantification for CMTs may require theory-error estimation which becomes a problem of specifying noise models. Various noise models have been proposed, and these rely on several assumptions. All approaches quantify theory errors by estimating the covariance matrix of data residuals. However, this estimation can be based on explicit modelling, empirical estimation and/or ignore or include covariances. We quantitatively compare several approaches by presenting parameter and uncertainty estimates in nonlinear full CMT estimation for several simulated data sets and regional field data of the Ml 4.4, 2015 June 13 Fox Creek, Canada, event. While our main focus is at regional distances, the tested approaches are general and implemented for arbitrary source model choice. These include known or unknown centroid locations, full MTs, deviatoric MTs and double-couple MTs. We demonstrate that velocity-model uncertainties can profoundly affect parameter estimation and that their inclusion leads to more realistic parameter uncertainty quantification. However, not all approaches perform equally well. Including theory errors by estimating non-stationary (non-Toeplitz) error covariance matrices via iterative schemes during Monte Carlo sampling performs best and is computationally most efficient. In general, including velocity-model uncertainties is most important in cases where velocity structure is poorly known.

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Hidayati, Lilik, Nur Chamidah, and I. Nyoman Budiantara. "ESTIMASI SELANG KEPERCAYAAN NILAI UJIAN NASIONAL BERBASIS KOMPETENSI BERDASARKAN MODEL REGRESI SEMIPARAMETRIK MULTIRESPON TRUNCATED SPLINE." MEDIA STATISTIKA 13, no. 1 (June 25, 2020): 92–103. http://dx.doi.org/10.14710/medstat.13.1.92-103.

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Confidence interval estimation is important in statistical inference for the parameters of the regression model, but the theory of confidence interval estimation for multi-response semiparametric regression model parameters based on the truncated spline estimator has not been examined. In this study, we estimate the confidence interval of the multi-response semiparametric regression model based on the truncated spline estimator by using pivotal quantity method with the central limit theorem approach. This confidence interval theory is applied to data of competency-based national exam (UNBK) scores in West Nusa Tenggara Province where its UNBK in the lowest position among other provinces in Indonesia. The method used for estimating parameters is weighted least square. The best model is determined based on the Generalized Cross Validation (GCV) minimum value. Based on the estimated 95% confidence interval of parameters of the multi-response truncated spline semiparametric regression model, the results showed that the insignificant factors affecting the UNBK scores were gender and parental education duration while the report card of scores and USBK scores had a positive effect on the UNBK scores but only the UNBK scores of mathematics that report card of scores factor has a negative effect on it.

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Zinde-Walsh, Victoria. "KERNEL ESTIMATION WHEN DENSITY MAY NOT EXIST." Econometric Theory 24, no. 3 (February 26, 2008): 696–725. http://dx.doi.org/10.1017/s0266466608080298.

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Nonparametric kernel estimation of density and conditional mean is widely used, but many of the pointwise and global asymptotic results for the estimators are not available unless the density is continuous and appropriately smooth; in kernel estimation for discrete-continuous cases smoothness is required for the continuous variables. Nonsmooth density and mass points in distributions arise in various situations that are examined in empirical studies; some examples and explanations are discussed in the paper. Generally, any distribution function consists of absolutely continuous, discrete, and singular components, but only a few special cases of nonparametric estimation involving singularity have been examined in the literature, and asymptotic theory under the general setup has not been developed. In this paper the asymptotic process for the kernel estimator is examined by means of the generalized functions and generalized random processes approach; it provides a unified theory because density and its derivatives can be defined as generalized functions for any distribution, including cases with singular components. The limit process for the kernel estimator of density is fully characterized in terms of a generalized Gaussian process. Asymptotic results for the Nadaraya–Watson conditional mean estimator are also provided.

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Daouia, Abdelaati, Jean-Pierre Florens, and Léopold Simar. "Frontier estimation and extreme value theory." Bernoulli 16, no. 4 (November 2010): 1039–63. http://dx.doi.org/10.3150/10-bej256.

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Ackerman, Terry A., and Frank B. Baker. "Item Response Theory: Parameter Estimation Techniques." Journal of the American Statistical Association 88, no. 422 (June 1993): 707. http://dx.doi.org/10.2307/2290371.

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Journal articles on the topic 'Estimation theory'

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