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Journal articles on the topic 'Optimal estimation of parameters'

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Author: Grafiati

Published: 6 September 2023

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1

Bashier, Eihab B. M. "Estimation of the Optimal Regularization Parameters in Optimal Control Problems with time delay." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 9 (September 21, 2016): 6589–602. http://dx.doi.org/10.24297/jam.v12i9.129.

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In this paper we use the L-curve method and the Morozov discrepancy principle for the estimation of the regularization parameter in the regularization of time-delayed optimal control computation. Zeroth order, first order and second order differential operators are considered. Two test examples show that the L-curve method and the two discrepancy principles give close estimations for the regularization parameters.

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2

Banks, H. T., and K. L. Rehm. "PARAMETER ESTIMATION IN DISTRIBUTED SYSTEMS: OPTIMAL DESIGN." Eurasian Journal of Mathematical and Computer Applications 2, no. 1 (2014): 70–80. http://dx.doi.org/10.32523/2306-3172-2014-2-1-70-80.

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3

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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4

Brack, A. "Optimal Estimation of a Subset of Integers with Application to GNSS." Artificial Satellites 51, no. 4 (December 1, 2016): 123–34. http://dx.doi.org/10.1515/arsa-2016-0011.

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Abstract The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive Gaussian measurement noise the integer least-squares estimator is optimal in the sense of maximizing the probability of correctly estimating the full vector of integer parameters. In applications such as global navigation satellite system ambiguity resolution, it can be beneficial to resolve only a subset of all integer parameters. We derive the estimator that leads to the highest possible success rate for a given integer subset and compare its performance to suboptimal integer mappings via numerical studies. Implementation aspects of the optimal estimator as well as subset selection criteria are discussed.

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Cummins, Donald P., David B. Stephenson, and Peter A. Stott. "Optimal Estimation of Stochastic Energy Balance Model Parameters." Journal of Climate 33, no. 18 (September 15, 2020): 7909–26. http://dx.doi.org/10.1175/jcli-d-19-0589.1.

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AbstractThis study has developed a rigorous and efficient maximum likelihood method for estimating the parameters in stochastic energy balance models (with any k > 0 number of boxes) given time series of surface temperature and top-of-the-atmosphere net downward radiative flux. The method works by finding a state-space representation of the linear dynamic system and evaluating the likelihood recursively via the Kalman filter. Confidence intervals for estimated parameters are straightforward to construct in the maximum likelihood framework, and information criteria may be used to choose an optimal number of boxes for parsimonious k-box emulation of atmosphere–ocean general circulation models (AOGCMs). In addition to estimating model parameters the method enables hidden state estimation for the unobservable boxes corresponding to the deep ocean, and also enables noise filtering for observations of surface temperature. The feasibility, reliability, and performance of the proposed method are demonstrated in a simulation study. To obtain a set of optimal k-box emulators, models are fitted to the 4 × CO2 step responses of 16 AOGCMs in CMIP5. It is found that for all 16 AOGCMs three boxes are required for optimal k-box emulation. The number of boxes k is found to influence, sometimes strongly, the impulse responses of the fitted models.

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6

Kates, James M. "Optimal estimation of hearing‐aid compression parameters." Journal of the Acoustical Society of America 94, no. 1 (July 1993): 1–12. http://dx.doi.org/10.1121/1.407078.

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7

NAKAMURA, Masahide. "Estimation of Optimal Parameters in Tchebychev Iteration." Transactions of the Japan Society of Mechanical Engineers Series C 65, no. 636 (1999): 3181–88. http://dx.doi.org/10.1299/kikaic.65.3181.

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8

Abdul Jalil, Nur Raihan, Nur Anisah Mohamed, and Rossita Mohamad Yunus. "Estimation in regret-regression using quadratic inference functions with ridge estimator." PLOS ONE 17, no. 7 (July 21, 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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9

Sugiyama, Takatoshi, and Toru Ogura. "Parameters Estimation for Wear-out Failure Period of Three-Parameter Weibull Distribution." International Journal of Statistics and Probability 11, no. 1 (December 26, 2021): 40. http://dx.doi.org/10.5539/ijsp.v11n1p40.

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The shape parameter estimation using the minimum-variance linear estimator with hyperparameter (MVLE-H) method is believed to be effective for a wear-out failure period in a small sample. In the process of the estimation, our method uses the hyperparameter and estimate shape parameters of the MVLE-H method. To obtain the optimal hyperparameter c, it takes a long time, even in the case of the small sample. The main purpose of this paper is to remove the restriction of small samples. We observed that if we set the shape parameters, for sample size n and c, we can use the regression equation to infer the optimal c from n. So we searched in five increments and complemented the hyperparameter for the remaining sample sizes with a linear regression line. We used Monte Carlo simulations (MCSs) to determine the optimal hyperparameter for various sample sizes and shape parameters of the MVLE-H method. Intrinsically, we showed that the MVLE-H method performs well by determining the hyperparameter. Further, we showed that the location and scale parameter estimations are improved using the shape parameter estimated by the MVLE-H method. We verified the validity of the MVLE-H method using MCSs and a numerical example.

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10

Ran, Mengfei, and Yihe Yang. "Optimal Estimation of Large Functional and Longitudinal Data by Using Functional Linear Mixed Model." Mathematics 10, no. 22 (November 17, 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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11

Hu, Cheng, Shaoyang Kong, Rui Wang, Fan Zhang, and Lianjun Wang. "Insect Mass Estimation Based on Radar Cross Section Parameters and Support Vector Regression Algorithm." Remote Sensing 12, no. 11 (June 11, 2020): 1903. http://dx.doi.org/10.3390/rs12111903.

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Radar cross section (RCS) parameters of insect targets contain information related to their morphological parameters, which are helpful for the identification of migratory insects. Several morphological parameter estimation methods have been presented. However, most of these estimations are performed based on polynomial fitting methods, using only one or two parameters, which may limit the estimation accuracy. In this paper, a new insect mass estimation method is proposed based on support vector regression (SVR). Several RCS parameters were extracted for the estimation of insect mass. Support vector regression based on recursive feature elimination (SVRRFE) was used to obtain the optimal feature subset. Specifically, a dataset including 367 specimens was included to evaluate the performance of the proposed method. Fifteen features were extracted and ranked. The optimal feature subset contained six features and the optimal mass estimation accuracy was 78%. Additionally, traditional insect mass estimation methods were analyzed for comparison. The results prove that the proposed method is more effective and accurate for insect mass estimation. It needs to be emphasized that the poor number of experimental insects available may limit the further improvement of estimation accuracy.

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12

Narapusetty, Balachandrudu, Timothy DelSole, and Michael K. Tippett. "Optimal Estimation of the Climatological Mean." Journal of Climate 22, no. 18 (September 15, 2009): 4845–59. http://dx.doi.org/10.1175/2009jcli2944.1.

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Abstract This paper shows theoretically and with examples that climatological means derived from spectral methods predict independent data with less error than climatological means derived from simple averaging. Herein, “spectral methods” indicates a least squares fit to a sum of a small number of sines and cosines that are periodic on annual or diurnal periods, and “simple averaging” refers to mean averages computed while holding the phase of the annual or diurnal cycle constant. The fact that spectral methods are superior to simple averaging can be understood as a straightforward consequence of overfitting, provided that one recognizes that simple averaging is a special case of the spectral method. To illustrate these results, the two methods are compared in the context of estimating the climatological mean of sea surface temperature (SST). Cross-validation experiments indicate that about four harmonics of the annual cycle are adequate, which requires estimation of nine independent parameters. In contrast, simple averaging of daily SST requires estimation of 366 parameters—one for each day of the year, which is a factor of 40 more parameters. Consistent with the greater number of parameters, simple averaging poorly predicts samples that were not included in the estimation of the climatological mean, compared to the spectral method. In addition to being more accurate, the spectral method also accommodates leap years and missing data simply, results in a greater degree of data compression, and automatically produces smooth time series.

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13

Zhang, Yan, Jiyuan Tao, Zhixiang Yin, and Guoqiang Wang. "Improved Large Covariance Matrix Estimation Based on Efficient Convex Combination and Its Application in Portfolio Optimization." Mathematics 10, no. 22 (November 16, 2022): 4282. http://dx.doi.org/10.3390/math10224282.

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The estimation of the covariance matrix is an important topic in the field of multivariate statistical analysis. In this paper, we propose a new estimator, which is a convex combination of the linear shrinkage estimation and the rotation-invariant estimator under the Frobenius norm. We first obtain the optimal parameters by using grid search and cross-validation, and then, we use these optimal parameters to demonstrate the effectiveness and robustness of the proposed estimation in the numerical simulations. Finally, in empirical research, we apply the covariance matrix estimation to the portfolio optimization. Compared to the existing estimators, we show that the proposed estimator has better performance and lower out-of-sample risk in portfolio optimization.

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14

Liang, Y., A. Thavaneswaran, and B. Abraham. "Joint Estimation Using Quadratic Estimating Function." Journal of Probability and Statistics 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/372512.

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A class of martingale estimating functions is convenient and plays an important role for inference for nonlinear time series models. However, when the information about the first four conditional moments of the observed process becomes available, the quadratic estimating functions are more informative. In this paper, a general framework for joint estimation of conditional mean and variance parameters in time series models using quadratic estimating functions is developed. Superiority of the approach is demonstrated by comparing the information associated with the optimal quadratic estimating function with the information associated with other estimating functions. The method is used to study the optimal quadratic estimating functions of the parameters of autoregressive conditional duration (ACD) models, random coefficient autoregressive (RCA) models, doubly stochastic models and regression models with ARCH errors. Closed-form expressions for the information gain are also discussed in some detail.

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15

Gulyaev, Yu V., S. V. Panasenko, A. A. Potapov, and L. F. Chernogor. "Optimal detection and optimal estimation of parameters of the envelope soliton." Doklady Physics 56, no. 2 (February 2011): 73–77. http://dx.doi.org/10.1134/s102833581102008x.

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16

Sun, Danna, Zhaoying Jiang, and Ziku Wu. "Optimal Estimation of Parameters for an HIV Model." Engineering 05, no. 10 (2013): 413–15. http://dx.doi.org/10.4236/eng.2013.510b084.

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17

Nevistić, Vesna, and Sadko Mandzuka. "Optimal Estimation of the Parameters for Ship Navigation." IFAC Proceedings Volumes 28, no. 2 (May 1995): 223–29. http://dx.doi.org/10.1016/s1474-6670(17)51675-4.

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18

Doungpan, Satawat, Vanvisa Chatchavong, and Kanok Janchitrapongvej. "Applicability of Weibull distribution in Generating Model for Evaluating Lifespan Closed Circuit Television System (CCTV)." Journal of Physics: Conference Series 2559, no. 1 (August 1, 2023): 012007. http://dx.doi.org/10.1088/1742-6596/2559/1/012007.

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Abstract CCTV is an expedient tool for monitoring and investigating. Since it can record emergency and routine events in memory of the electronic circuit board. However, in the process of operating CCTV, it is necessary to carry out a sampling inspection on its lifetime to predicate its availability and reliability. According to previous literature, most of the parameter estimation methods used only one parameter estimation method, which is not sufficient for identifying two explicit parameters of Weibull distribution. Moreover, the bad parameter estimation method cannot achieve reliable analysis results. Therefore, this paper presented the four methods of estimation in both graphical and analytical methods for estimating parameters of Weibull distribution. These methods have measured the accuracy by using mean square error (MSE). In addition, the real data set confirmed that there is the Weibull distribution by using the Kolmogorov-Smirnov test. The simulation results found that the maximum likelihood method (MLM) can outperform the other estimator because it can provide a minimum MSE, there is an optimal parameter in which the shape is 4.3881 and the scale is 86.8207. Finally, the two optimal parameters are applied to real data sets of the CCTV. As a result, the optimal parameter fits with real data sets, and it can evaluate the lifespan of CCTV by using the mean time to failure (MTTF) as 6.6 years.

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19

Zhong, Xun Yu, Xiao Shan Li, and Yong Gang Zhao. "Model Parameters Estimation for Image Motion Compensation." Applied Mechanics and Materials 347-350 (August 2013): 3672–76. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.3672.

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Fast and optimal motion estimation method is proposed for electronic image stabilization. First, an approach for macro-block judgment is presented. Before motion vectors calculation, gradient information is analyzed, only useful reference blocks that are indispensable for accurate motion estimation are selected, by which the number of macro-blocks for subsequent calculation is reduced. Second, in the block matching, an improved SSDA is used to reduce computing cost. Finally, the affine transformation model and similarity transformation model of image motion are created and using least squares method for solving the optimal estimation of model parameters. Experimental results show the accuracy and fast computing speed of the proposed method.

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20

Wang, Zhenyu, Hana Sheikh, Kyongbum Lee, and Christos Georgakis. "Sequential Parameter Estimation for Mammalian Cell Model Based on In Silico Design of Experiments." Processes 6, no. 8 (July 24, 2018): 100. http://dx.doi.org/10.3390/pr6080100.

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Due to the complicated metabolism of mammalian cells, the corresponding dynamic mathematical models usually consist of large sets of differential and algebraic equations with a large number of parameters to be estimated. On the other hand, the measured data for estimating the model parameters are limited. Consequently, the parameter estimates may converge to a local minimum far from the optimal ones, especially when the initial guesses of the parameter values are poor. The methodology presented in this paper provides a systematic way for estimating parameters sequentially that generates better initial guesses for parameter estimation and improves the accuracy of the obtained metabolic model. The model parameters are first classified into four subsets of decreasing importance, based on the sensitivity of the model’s predictions on the parameters’ assumed values. The parameters in the most sensitive subset, typically a small fraction of the total, are estimated first. When estimating the remaining parameters with next most sensitive subset, the subsets of parameters with higher sensitivities are estimated again using their previously obtained optimal values as the initial guesses. The power of this sequential estimation approach is illustrated through a case study on the estimation of parameters in a dynamic model of CHO cell metabolism in fed-batch culture. We show that the sequential parameter estimation approach improves model accuracy and that using limited data to estimate low-sensitivity parameters can worsen model performance.

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21

Shmatko, Olexandr, Valerii Volosyuk, Simeon Zhyla, Vladimir Pavlikov, Nikolay Ruzhentsev, Eduard Tserne, Anatoliy Popov, et al. "Synthesis of the optimal algorithm and structure of contactless optical device for estimating the parameters of statistically uneven surfaces." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 4 (November 29, 2021): 199–213. http://dx.doi.org/10.32620/reks.2021.4.16.

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The production of parts and (or) finished products in electronics, mechanical engineering and other industries is inextricably linked with the control of the accuracy and cleanliness of the processed surfaces. Currently existing meters of parameters of statistically uneven surfaces, both contact and non-contact have some disadvantages, as well as limitations due to methods and design features of measurement. Speckle interferometric methods for measuring parameters of statistically uneven surfaces make it possible to get away from some disadvantages inherent in existing methods and measurements. The use of methods of statistical radio engineering, methods of optimization of statistical solutions and estimates of parameters of predictive distributions for optimal radio engineering system synthesis is promising for the analysis and processing optical-electronic coherent laser space-time signals (speckle images) form with the laser radiation scattered by statistically uneven surfaces. This work synthesizes the optimal algorithm and structure for analyzing the parameters of statistically-temporal surfaces based on spatio-temporal processing of optical speckle interference signals and images using modern methods of optimal synthesis of radio engineering and coherent optoelectronic systems. In this work, an algorithm for processing optical signals scattered by statistically uneven surfaces is synthesized and investigated for problems of optimal estimation of parameters and statistical characteristics of statistically uneven surfaces. A block diagram of the optical contactless device for evaluating the parameters of statistically uneven surfaces is proposed. The limiting errors of estimation parameters of statistically uneven surfaces and the optimal installation angles of the emitters and the optical receiver are investigated. Equations are obtained for estimating the root-mean-square height of the ridges and the correlation radius of small-scale statistically uneven surfaces in the approximation of small perturbations. The proposed method for evaluating the parameters of statistically uneven surfaces allows to increase the accuracy of measurements, to conduct a non-contact assessment of the parameters - even statistically uneven surfaces that have geometric surface irregularities or located in hard-to-reach places, for example, grooves, holes, as well as products of cylindrical, spherical and other shapes.

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22

Apasov, R. T., R. R. Badgutdinov, A. I. Varavva, F. A. Koryakin, S. A. Nekhaev, I. V. Perevozkin, D. A. Samolovov, E. E. Sandalova, and A. F. Yamaletdinov. "Estimation of optimal parameters for gas field development system." Neftyanoe khozyaystvo - Oil Industry, no. 12 (2021): 74–78. http://dx.doi.org/10.24887/0028-2448-2021-12-74-78.

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23

Hudson, Derek, and David G. Long. "Optimal Estimation of Calibration Parameters in Polarimetric Microwave Radiometers." IEEE Transactions on Geoscience and Remote Sensing 46, no. 10 (October 2008): 3223–37. http://dx.doi.org/10.1109/tgrs.2008.921636.

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24

Virzì, S., A. Avella, F. Piacentini, M. Gramegna, G. Brida, I. P. Degiovanni, and M. Genovese. "Optimal estimation of parameters of an entangled quantum state." Journal of Physics: Conference Series 841 (May 2017): 012033. http://dx.doi.org/10.1088/1742-6596/841/1/012033.

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25

White, Luther W., Baxter Vieux, David Armand, and Francois X. LeDimet. "Estimation of optimal parameters for a surface hydrology model." Advances in Water Resources 26, no. 3 (March 2003): 337–48. http://dx.doi.org/10.1016/s0309-1708(02)00189-6.

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26

Shen, Jian. "Optimal estimation of parameters for a estuarine eutrophication model." Ecological Modelling 191, no. 3-4 (February 2006): 521–37. http://dx.doi.org/10.1016/j.ecolmodel.2005.05.020.

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27

Cui, Yuntao, John Weng, and Herbert Reynolds. "Estimation of ellipse parameters using optimal minimum variance estimator." Pattern Recognition Letters 17, no. 3 (March 1996): 309–16. http://dx.doi.org/10.1016/0167-8655(95)00114-x.

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28

Petković, Dalibor, Nenad T. Pavlović, Shahaboddin Shamshirband, Miss Laiha Mat Kiah, Nor Badrul Anuar, and Mohd Yamani Idna Idris. "Adaptive neuro-fuzzy estimation of optimal lens system parameters." Optics and Lasers in Engineering 55 (April 2014): 84–93. http://dx.doi.org/10.1016/j.optlaseng.2013.10.018.

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29

Zakerzadeh, Hojatollah, Ali Akbar Jafari, and Mahdieh Karimi. "Optimal Shrinkage Estimations for the Parameters of Exponential Distribution Based on Record Values." Revista Colombiana de Estadística 39, no. 1 (January 18, 2016): 33–44. http://dx.doi.org/10.15446/rce.v39n1.55137.

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<p>This paper studies shrinkage estimation after the preliminary test for the parameters of exponential distribution based on record values. The optimal value of shrinkage coefficients is also obtained based on the minimax regret criterion. The maximum likelihood, pre-test, and shrinkage estimators are compared using a simulation study. The results to estimate the scale parameter show that the optimal shrinkage estimator is better than the maximum likelihood estimator in all cases, and when the prior guess is near the true value, the pre-test estimator is better than shrinkage estimator. The results to estimate the location parameter show that the optimal shrinkage estimator is better than maximum likelihood estimator when a prior guess is close<br />to the true value. All estimators are illustrated by a numerical example.</p>

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30

Li, Yi Qiang, and Zhi Qiang Huang. "A New Framework for Myocardium Constitutive Parameters Estimation." Applied Mechanics and Materials 876 (February 2018): 128–32. http://dx.doi.org/10.4028/www.scientific.net/amm.876.128.

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In this study, a new inverse analysis framework for estimation of myocardium constitutive parameters is established. In this framework, by using cardiac magnetic resonance image of realistic human left ventricular, a more realistic, finite element analysis model for analyzing the deformation of left ventricle during diastole is introduced. The anisotropic nonlinear Holzapfel-Ogden constitutive model is used to describe the material behavior of myocardium. Estimating the parameters as for the inverse problem of left ventricle deformation, a novel hybrid simplex and particle swarm optimization algorithm is proposed to estimate the parameters of myocardium’s constitutive model. Numerical examples presents that finite element analysis results and the estimated parameters are in good agreement with the experimental data reported in literature, comparing with current optimization algorithm, the presented hybrid optimal algorithm can estimate the constitutive parameters more efficient. The efficiency and validity of the proposed parameter estimation framework is demonstrated.

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31

Zhong, Xun Yu, and Tian Hui Ren. "Motion Model Parameters Estimation for Electronic Image Stabilization Instrument." Applied Mechanics and Materials 325-326 (June 2013): 1543–46. http://dx.doi.org/10.4028/www.scientific.net/amm.325-326.1543.

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Fast and optimal motion estimation method is proposed for electronic image stabilization. First, an approach for macro-block judgment is presented. Before motion vectors calculation, gradient information is analyzed, only useful reference blocks that are indispensable for accurate motion estimation are selected, by which the number of macro-blocks for subsequent calculation is reduced. Second, in the block matching, an improved SSDA is used to reduce computing cost. Finally, the affine transformation model and similarity transformation model of image motion are created and using least squares method for solving the optimal estimation of model parameters. Experimental results show the accuracy and fast computing speed of the proposed method.

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32

CHIRIBELLA, GIULIO, GIACOMO MAURO D'ARIANO, PAOLO PERINOTTI, and MASSIMILIANO F. SACCHI. "MAXIMUM LIKELIHOOD ESTIMATION FOR A GROUP OF PHYSICAL TRANSFORMATIONS." International Journal of Quantum Information 04, no. 03 (June 2006): 453–72. http://dx.doi.org/10.1142/s0219749906002018.

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The maximum likelihood strategy for the estimation of group parameters allows one to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results provide deep insight into the general structure underlying optimal quantum estimation strategies. The entanglement between representation spaces and multiplicity spaces of the group action appears to be the unique kind of entanglement which is really useful for the optimal estimation of group parameters.

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33

Marin, Carlos M. "Parameter Estimation in Water Resources Planning and Management: Optimal Actions or Optimal Parameters?" Water Resources Research 22, no. 3 (March 1986): 353–60. http://dx.doi.org/10.1029/wr022i003p00353.

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34

Tang, Hesheng, Xueyuan Guo, Liyu Xie, and Songtao Xue. "Experimental Validation of Optimal Parameter and Uncertainty Estimation for Structural Systems Using a Shuffled Complex Evolution Metropolis Algorithm." Applied Sciences 9, no. 22 (November 18, 2019): 4959. http://dx.doi.org/10.3390/app9224959.

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The uncertainty in parameter estimation arises from structural systems’ input and output measured errors and from structural model errors. An experimental verification of the shuffled complex evolution metropolis algorithm (SCEM-UA) for identifying the optimal parameters of structural systems and estimating their uncertainty is presented. First, the estimation framework is theoretically developed. The SCEM-UA algorithm is employed to search through feasible parameters’ space and to infer the posterior distribution of the parameters automatically. The resulting posterior parameter distribution then provides the most likely estimation of parameter sets that produces the best model performance. The algorithm is subsequently validated through both numerical simulation and shaking table experiment for estimating the parameters of structural systems considering the uncertainty of available information. Finally, the proposed algorithm is extended to identify the uncertain physical parameters of a nonlinear structural system with a particle mass tuned damper (PTMD). The results demonstrate that the proposed algorithm can effectively estimate parameters with uncertainty for nonlinear structural systems, and it has a stronger anti-noise capability. Notably, the SCEM-UA method not only shows better global optimization capability compared with other heuristic optimization methods, but it also has the ability to simultaneously estimate the uncertainties associated with the posterior distributions of the structural parameters within a single optimization run.

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35

Xiang, Huili, and Zhijun Liu. "The Optimal Control and MLE of Parameters of a Stochastic Single-Species System." Discrete Dynamics in Nature and Society 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/676871.

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This paper investigates the optimal control and MLE (maximum likelihood estimation) for a single-species system subject to random perturbation. With the help of the techniques of stochastic analysis and mathematical statistics, sufficient conditions for the optimal control threshold value, the optimal control moment, and the maximum likelihood estimation of parameters are established, respectively. An example is presented to illustrate the feasibility of our theoretical results.

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36

Mohammed, M. A., Sundus N. Al-Aziz, Eateraf M. A. Al Sumati, and Emad E. Mahmoud. "Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function." Computational Intelligence and Neuroscience 2022 (April 30, 2022): 1–12. http://dx.doi.org/10.1155/2022/4822212.

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The LINEX loss function, which climbs exponentially with one-half of zero and virtually linearly on either side of zero, is employed to analyze parameter analysis and prediction problems. It can be used to solve both underestimation and overestimation issues. This paper explained the Bayesian estimation of mean, Gamma distribution, and Poisson process. First, an improved estimator for μ 2 is provided (which employs a variation coefficient). Under the LINEX loss function, a better estimator for the square root of the median is also derived, and an enhanced estimation for the average mean in such a negatively exponential function. Second, giving a gamma distribution as a prior and a likelihood function as posterior yields a gamma distribution. The LINEX method can be used to estimate an estimator λ B L ^ using posterior distribution. After obtaining λ B L ^ , the hazard function h B L ^ and D B L ^ the function of survival estimators are used. Third, the challenge of sequentially predicting the intensity variable of a uniform Poisson process with a linear exponentially (LINEX) loss function and a constant cost of production time is investigated using a Bayesian model. The APO rule is offered as an approximation pointwise optimal rule. LINEX is the loss function used. A variety of prior distributions have already been studied, and Bayesian estimation methods have been evaluated against squared error loss function estimation methods. Finally, compare the results of Maximum Likelihood Estimation (MLE) and LINEX estimation to determine which technique is appropriate for such information by identifying the lowest Mean Square Error (MSE). The displaced estimation method under the LINEX loss function was also examined in this research, and an improved estimation was proposed.

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Gianani, Ilaria, and Claudia Benedetti. "Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning." AVS Quantum Science 5, no. 1 (March 2023): 014405. http://dx.doi.org/10.1116/5.0137398.

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The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum walks, the parameters themselves may not be directly accessible, and, thus, it is necessary to find alternative estimation strategies exploiting other observables. Here, we perform the multiparameter estimation of the Hamiltonian parameters characterizing a continuous-time quantum walk over a line graph with n-neighbor interactions using a deep neural network model fed with experimental probabilities at a given evolution time. We compare our results with the bounds derived from estimation theory and find that the neural network acts as a nearly optimal estimator both when the estimation of two or three parameters is performed.

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Fu, Y. X., and W. H. Li. "Maximum likelihood estimation of population parameters." Genetics 134, no. 4 (August 1, 1993): 1261–70. http://dx.doi.org/10.1093/genetics/134.4.1261.

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Abstract One of the most important parameters in population genetics is theta = 4Ne mu where Ne is the effective population size and mu is the rate of mutation per gene per generation. We study two related problems, using the maximum likelihood method and the theory of coalescence. One problem is the potential improvement of accuracy in estimating the parameter theta over existing methods and the other is the estimation of parameter lambda which is the ratio of two theta's. The minimum variances of estimates of the parameter theta are derived under two idealized situations. These minimum variances serve as the lower bounds of the variances of all possible estimates of theta in practice. We then show that Watterson's estimate of theta based on the number of segregating sites is asymptotically an optimal estimate of theta. However, for a finite sample of sequences, substantial improvement over Watterson's estimate is possible when theta is large. The maximum likelihood estimate of lambda = theta 1/theta 2 is obtained and the properties of the estimate are discussed.

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Mahmoud, Magdi S., and Peng Shi. "Optimal guaranteed cost filtering for Markovian jump discrete-time systems." Mathematical Problems in Engineering 2004, no. 1 (2004): 33–48. http://dx.doi.org/10.1155/s1024123x04108016.

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This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

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Hopkins, M. A., and H. F. VanLandingham. "Optimal Nonlinear Estimation of Linear Stochastic Systems." Journal of Dynamic Systems, Measurement, and Control 116, no. 3 (September 1, 1994): 529–36. http://dx.doi.org/10.1115/1.2899248.

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This paper presents a new nonlinear method of simultaneous parameter and state estimation called pseudo-linear identification (PLID), for stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer function must be strictly proper. Under standard gaussian assumptions, for completely controllable and observable systems, it is proved that PLID is the minimum mean-square-error estimator of the states and model parameters, conditioned on the input and output measurements. It is also proved, given persistent excitation, that the parameter estimates converge a.e. to the true parameter values. All results have been extended to the multiple-input, multiple-output case, but the single-input, single-output case is presented here to simplify notation.

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Yan, Li, Chen Yang, and Chuan Bing Ding. "An Optimal Estimation of Aerodynamic Parameters for GPS Guided Missile." Applied Mechanics and Materials 325-326 (June 2013): 734–37. http://dx.doi.org/10.4028/www.scientific.net/amm.325-326.734.

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The disturbance factors in the missile flight are obvious,so the analytical equations of missile longitudinal disturbance of movement is derived . The missile body longitudinal aerodynamic parameters are fitting out with wind tunnel experimental data. The equation of system state takes the aerodynamic coefficient errors interference source and GPS error sources as the state variables, and the system measurement equation adopts GPS pseudo-range measurements. In passive segment, the aerodynamic coefficients disturbing errors sources of th missile longitudinal plane is estimated optimally with extended Kalman filter. The results show that the method accelerate the convergence speed of the disturbance source errors, and improve the estimation accuracy of the perturbation errors.

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Shaw, A. K. "Optimal estimation of the parameters of all-pole transfer functions." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 41, no. 2 (1994): 140–50. http://dx.doi.org/10.1109/82.281845.

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Vasudeva Rao, A., A. V. Dattatreya Rao, and V. L. Narasimham. "Asymptotically optimal grouping for maximum likelihood estimation of weibull parameters." Communications in Statistics - Simulation and Computation 23, no. 4 (January 1994): 1077–96. http://dx.doi.org/10.1080/03610919408813218.

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Alexander, Daniel C., and Gareth J. Barker. "Optimal imaging parameters for fiber-orientation estimation in diffusion MRI." NeuroImage 27, no. 2 (August 2005): 357–67. http://dx.doi.org/10.1016/j.neuroimage.2005.04.008.

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Alirezazadeh, Pantea, Fidan Boylu, Robert Garfinkel, Ram Gopal, and Paulo Goes. "Identity matching and information acquisition: Estimation of optimal threshold parameters." Decision Support Systems 57 (January 2014): 160–71. http://dx.doi.org/10.1016/j.dss.2013.08.014.

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Theeuwes, J., C. C. Koopmans, R. Van Opstal, and H. Van Reijn. "Estimation of optimal human capital accumulation parameters for The Netherlands." European Economic Review 29, no. 2 (January 1985): 233–57. http://dx.doi.org/10.1016/0014-2921(85)90054-6.

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Jankumas, A. "Optimal adaptive control for estimation of parameters of ARX models." IEEE Transactions on Automatic Control 45, no. 5 (May 2000): 964–68. http://dx.doi.org/10.1109/9.855561.

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Yusup, Norfadzlan, Arezoo Sarkheyli, Azlan Mohd Zain, Siti Zaiton Mohd Hashim, and Norafida Ithnin. "Estimation of optimal machining control parameters using artificial bee colony." Journal of Intelligent Manufacturing 25, no. 6 (March 14, 2013): 1463–72. http://dx.doi.org/10.1007/s10845-013-0753-y.

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Arnhem, Matthieu, Evgueni Karpov, and Nicolas J. Cerf. "Optimal Estimation of Parameters Encoded in Quantum Coherent State Quadratures." Applied Sciences 9, no. 20 (October 11, 2019): 4264. http://dx.doi.org/10.3390/app9204264.

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In the context of multiparameter quantum estimation theory, we investigate the construction of linear schemes in order to infer two classical parameters that are encoded in the quadratures of two quantum coherent states. The optimality of the scheme built on two phase-conjugate coherent states is proven with the saturation of the quantum Cramér–Rao bound under some global energy constraint. In a more general setting, we consider and analyze a variety of n-mode schemes that can be used to encode n classical parameters into n quantum coherent states and then estimate all parameters optimally and simultaneously.

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López, Alberto, José Luis Olazagoitia, Francisco Marzal, and María Rosario Rubio. "Optimal parameter estimation in semi-empirical tire models." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 233, no. 1 (June 19, 2018): 73–87. http://dx.doi.org/10.1177/0954407018779851.

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Semi-empirical tire models are mathematical models, the parameters of which are identified after a process of error reduction to fit experimental data obtained in the laboratory. In this process, the algorithms used for estimating the model parameters are usually based on nonlinear least-squares fitting methods, in which only vertical residuals between the model and the test points are considered. Although extensively utilized, this type of fitting implicitly considers that errors in the slip data (horizontal residuals) are either nonexistent or negligible, which is not true. This paper introduces a new methodology to the identification of semi-empirical tire model parameters based on weighed orthogonal residuals, which takes into account possible errors inherent in the test measurements of dependent and independent variables. The results show that the methodology offers a reliable parameter identification providing an even fitting for all the zones of the mathematical semi-empirical tire model.

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