Estimators for the linear regression model based on Winsorized observations
Chen, L-A., Welsh, A.H. and Chan, W. (2001) Estimators for the linear regression model based on Winsorized observations. Statistica Sinica, 11, (1), 31-53.
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We develop an asymptotic, robust version of the Gauss-Markov theorem for estimating the regression parameter vector ćβ and a parametric function ćβ in the linear regression model. In a class of estimators for estimating ćβ that are linear in a Winsorized observation vector introduced by Welsh (1987), we show that Welsh's trimmed mean has smallest asymptotic covariance matrix. Also, for estimating a parametric function ćβ, the inner product of ć and the trimmed mean has the smallest asymptotic variance among a class of estimators linear in the Winsorized observation vector. A generalization of the linear Winsorized mean to the multivariate context is also given. Examples analyzing American lobster data and the mineral content of bones are used to compare the robustness of some trimmed mean methods.
|Keywords:||linear regression, robust estimation, trimmed mean, winsorized mean|
|Subjects:||Q Science > QA Mathematics
H Social Sciences > HA Statistics
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Statistics
|Date Deposited:||11 May 2006|
|Last Modified:||01 Jun 2011 16:32|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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