Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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A Study on a One-step Pairwise GM-estimator in Linear Models

  • Song, Moon-Sup (Department of Statistics, Seoul National University, Seoul, 151-742) ;
  • Kim, Jin-Ho (Korea Research Institute of Standards and Science, Taejon, 305-606)
  • Published : 1997.03.01
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Abstract

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

Keywords

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