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Estimators for the linear regression model based on Winsorized observations

Record type: Article

We develop an asymptotic, robust version of the Gauss-Markov theorem for estimating the regression parameter vector ?? and a parametric function ?? in the linear regression model. In a class of estimators for estimating ?? 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 ??, the inner product of ? 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.

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Citation

Chen, L-A., Welsh, A.H. and Chan, W. (2001) Estimators for the linear regression model based on Winsorized observations Statistica Sinica, 11, (1), pp. 31-53.

More information

Published date: 2001
Keywords: linear regression, robust estimation, trimmed mean, winsorized mean
Organisations: Statistics

Identifiers

Local EPrints ID: 29931
URI: http://eprints.soton.ac.uk/id/eprint/29931
ISSN: 1017-0405
PURE UUID: 2cf4bb41-3b98-4859-8d4d-96fdd1313884

Catalogue record

Date deposited: 11 May 2006
Last modified: 17 Jul 2017 15:56

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Contributors

Author: L-A. Chen
Author: A.H. Welsh
Author: W. Chan

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