Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Generalized M-Estimator in Linear Regression

  • Song, Moon-Sup (Department of Statistics, Seoul National University) ;
  • Park, Chang-Soon (Department of Applied Statistics, Chung-Ang University) ;
  • Nam, Ho-Soo (Graduate School of Seoul National University)
  • Published : 1994.12.01
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Abstract

We propose a robust regression estimator which has both a high breakdown point and a bounded influence function. The main contribution of this article is to present a weight function in the generalized M (GM)-estimator. The weighting schemes which control leverage points only without considering residuals cannot be efficient, since control leverage points only without considering residuals cannot be efficient, since these schemes inevitably downweight some good leverage points. In this paper we propose a weight function which depends both on design points and residuals, so as not to downweight good leverage points. Some motivating illustrations are also given.

Keywords

References

  1. Journal of the American Statistical Association v.88 A Bounded Influence, High Breakdown, Efficient Regression Estimator Coakley, C. W.;Hettmansperger, T. P.
  2. Robust Statistics: The Approach Based on Influence Functions Hampel, F. R.;Ronchetti, E. M.;Rousseeuw, P. J.;Stahel, W. A.
  3. Journal of the American Statistical Association v.77 Efficient Bounded-Influence Regression Estimation Krasker, W. S.;Welsch, R. E.
  4. Algorithm, Routines, and S Functions for Robust Statistics Marazzi, A.
  5. Journal of the American Statistical Association v.87 On One-Step GM Estimates and Stability of Inference in Linear Regression Simpson, D. G.;Ruppert, D.;Carroll, R. J.