Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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On the Robustness of $L_1$-estimator in Linear Regression Models

  • Bu-Yong Kim (Department of Statistics, Sookmyung Women's University, Seoul 140-742, KOREA)
  • Published : 1995.12.01
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Abstract

It is well kmown that the $L_1$-estimator is robust with respect to vertical outliers in regression data, even if it is susceptible to bad leverage points. This article is concerned with the robustness of the $L_1$-estimator. To investigate its robustness against vertical outliers we may find intervals for the value of the response variable within which the $L_1$-estimates do not shange. A procedure for constructing those intervals in multiple limear regression is illustrated in the sensitivity analysis context. And then vertical breakdown point of the $L_1$-estimator is defined on the basis of properties related to those intervals.

Keywords

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