Jointly Robust Estimation of Unknown Parameters and Variance Components Based on Expectation-Maximization Algorithm
Publication: Journal of Surveying Engineering
Volume 135, Issue 1
Abstract
Robust estimation of unknown parameters in linear models with only a single error component has been widely investigated. However only a small percentage of literature treats robust estimate of variance components in heteroscedastically mixed models. The correction-based pseudoobservation method, the -function-based robust maximum likelihood estimate (MLE) and restricted maximum likelihood estimate methods, as well as the robust Helmert method are the three kinds of typical robust methods for estimating variance components of linear mixed models. However, they are generally affected by different types of scoring functions and various tuning factors based on estimate defined by Huber from the maximum likelihood type of estimation. In addition, the pseudoobservation method will encounter risks of incorrect corrections due to the misidentification of gross errors. In this paper, gross errors and random or normal errors are assumed to be occasionally additive, independent, normally distributed with different scales, and all are regarded as missing and/or unobservable data. Together with the observations, they form a complete data problem where the unknown parameters and variance components need to be estimated. The expectation-maximization (EM) algorithm for finding the MLEs is robustified by estimating the variances of gross errors by defining weights and proposing to jointly solve the robust estimation of the unknown parameters and variance components. A numerical example of a global positioning system baseline network shows that the robustified EM algorithm can find a reliable estimate of unknown parameters and variance components, and efficiently separate the gross errors and subrandom effects or errors by computing their respective Bayesian estimate.
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Acknowledgments
This project was sponsored by “863” Project (2007AA12Z226), the Natural Science Foundation of China (40674015), the Natural Science Foundation of Key Laboratory of Dynamical Geodesy of Institute of Geodesy and Geophysics of Chinese Academy of Science (L06-01), the Natural Science Foundation of Chongqing (CSTC-2006BB0168). The writers are grateful to M. S. Yu Ling for her patient checking of the English of the manuscript and the three anonymous reviewers.
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Published In
Journal of Surveying Engineering
Volume 135 • Issue 1 • February 2009
Pages: 1 - 9
Copyright
© 2009 ASCE.
History
Received: Jun 29, 2007
Accepted: Apr 15, 2008
Published online: Feb 1, 2009
Published in print: Feb 2009
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