Estimators for the linear regression model based on winsorized observations

L. A. Chen*, A. H. Welsh, W. Chan

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    18 Citations (Scopus)

    Abstract

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

    Original languageEnglish
    Pages (from-to)147-172
    Number of pages26
    JournalStatistica Sinica
    Volume11
    Issue number1
    Publication statusPublished - Jan 2001

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