• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.1-22
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• 1997

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.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.471-487
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• 1996

In this paper we propose an efficient scoring type one-step GM-estimator, which has a bounded influence function and a high break-down point. The main point of the estimator is in the weighting scheme of the GM-estimator. The weight function we used depends on both leverage points and residuals So we construct an estimator which does not downweight good leverage points Unider some regularity conditions, we compute the finite-sample breakdown point and prove asymptotic normality Some simulation results are also presented.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.369-383
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• 1998

This paper deals with a robust regression estimator. We propose an efficient one-step GM-estimator, which has a bounded influence function and a high breakdown point. The main idea of this paper is to use the Mallows-type weights which depend on both the predictor variables and the residuals from a high breakdown initial estimator. The proposed weighting scheme severely downweights the bad leverage points and slightly downweights the good leverage points. Under some regularity conditions, we compute the finite-sample breakdown point and prove the asymptotic normality. Some simulation results and a numerical example are also presented.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.507-520
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• 1997

In this paper we propose a robust Wald-type test which is based on an efficient Mallows-type one-step GM-estimator. The proposed estimator based on the weight function of Song, Park and Nam (1996) has a bounded influence function and a high breakdown point. Under some regularity conditions, we compute the finite-sample breakdown point, and drive asymptotic normality of the proposed estimator. The level and power breakdown points, influence function and asymptotic distribution of the proposed test statistic are main points of this paper. To compare the performance of the proposed test with other tests, we perform some Monte Carlo simulations.