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Robust Variance Components Estimation in the PERG Mixed Distributions of Empirical Variances—PEROBVC Method
Department of Geodesy and Geoinformatics, Faculty of Civil Engineering, University of Belgrade, Belgrade, Serbia
- 1 Department of Geodesy and Geoinformatics, Faculty of Civil Engineering, University of Belgrade, Belgrade, Serbia
Open Journal of Statistics·Volume 10 (2020)·Pages 640–650·Published 10 July 2020·DOI10.4236/ojs.2020.104038
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Abstract
A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.
KeywordsNon-Homogeneous Sets of Empirical VariancesPERG Mixed Distribution of Empirical VariancesRobust Variance Components Estimation—PEROBVC Method
- Rao, C.R. and Kleffe, J. (1988) Estimation of Variance Components and Applications. North-Holland, Amsterdam.
- Krishnaiah, P.R., (1984) Analysis of Variance. North-Holland, Amsterdam.
- Harville, D.A. (1977) Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems. Journal of the American Statistical Association, 72, 320-338. https://doi.org/10.1080/01621459.1977.10480998
- Fellner, W.H. (1986) Robust Estimation of Variance Components. Technometrics, 28, 51-60. https://doi.org/10.1080/00401706.1986.10488097
- Robinson, D.L. (1987) Estimation and Use of Variance Components. Journal of the Royal Statistical Society. Series D (The Statistician), 36, 3-14. https://doi.org/10.2307/2988267
- Herbert, J.H. and Kott, Ph.S. (1988) Robust Variance Estimation in Linear Regression. Journal of Applied Statistics, 15, 341-345. https://doi.org/10.1080/02664768800000044
- Sidik, K. and Jonkman, J.N. (2006) Robust Variance Estimation for Random Effects Meta-Analysis. Computational Statistics & Data Analysis, 50, 3681-3701. https://doi.org/10.1016/j.csda.2005.07.019
- Hedges, L.V., Tipton, E. and Johnson, M.C. (2010) Robust Variance Estimation in Meta-Regression with Dependent Effect Size Estimates. Research Synthesis Methods, 1, 39-65. https://doi.org/10.1002/jrsm.5
- Koller, M. (2013) Robust Estimation of Linear Mixed Models. PhD Thesis, ETH, Zürich.
- Welsh, A.H. and Richardson, A.M. (1997) 13 Approaches to Robust Estimations of Mixed Models. In: Handbook of Statistics, Vol. 15, Elsevier Science, Amsterdam, 343-384. https://doi.org/10.1016/S0169-7161(97)15015-5
- Amiri-Simkooei, A.R. (2007) Least-Squares Variance Component Estimation: Theory and GPS Applications. Ph.D. Thesis, Delft University of Technology, Delft.
- Bartlett, J. (2014) The Robust Sandwich Variance Estimator for Linear Regression (Using R). The Stats Geek, February 14, 2014.
- Arango-Castillo, L. and Takahara, G. (2018) Robust Estimation of the Sample Mean Variance for Gaussian Processes with Long-Range Dependence. 2017 IEEE Global Conference on Signal and Information Processing, Montreal, 14-16 November 2017, 201-205. https://doi.org/10.1109/GlobalSIP.2017.8308632
- Chen, Y. and Jackson, D. (1995) Robust Estimation of Mean and Variance in Fisheries. Transactions of the American Fisheries Society, 124, 401-412. https://doi.org/10.1577/1548-8659(1995)124 2.3.CO;2