• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.27-32
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• 1994

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.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.541-550
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• 2010

The $L_1$-regression estimator is susceptible to the leverage points, even though it is highly robust to the vertical outliers. This article is concerned with the improvement of robustness of the $L_1$-estimator. To improve its robustness, in terms of the breakdown point, we attempt to dampen the influence of the leverage points by means of reducing the weights corresponding to the leverage points. In addition the algorithm employs the linear scaling transformation technique, for higher computational efficiency with the large data sets, to solve the linear programming problem of $L_1$-estimation. Monte Carlo simulation results indicate that the proposed algorithm yields $L_1$-estimates which are robust to the leverage points as well as the vertical outliers.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.97-110
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• 2006

Since it is well-established that even high quality data tend to contain outliers, one would expect fat? greater reliance on robust regression techniques than is actually observed. But most of all robust regression estimators suffers from the computational difficulties and the lower efficiency than the least squares under the normal error model. The weighted self-tuning estimator (WSTE) recently suggested by Lee (2004) has no more computational difficulty and it has the asymptotic normality and the high break-down point simultaneously. Although it has better properties than the other robust estimators, WSTE does not have full efficiency under the normal error model through the weighted least squares which is widely used. This paper introduces a new approach as called the reweighted WSTE (RWSTE), whose scale estimator is adaptively estimated by the self-tuning constant. A Monte Carlo study shows that new approach has better behavior than the general weighted least squares method under the normal model and the large data.

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.305-317
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• 2006

Outliers adversely affect model identification, parameter estimation, and forecast in time series data. In particular, when outliers consist of a patch of additive outliers, the current outlier detection procedures suffer from the masking and swamping effects which make them inefficient. In this paper, we propose new outlier detection procedure based on high breakdown estimators, called as the dual robust filtering. Empirical and simulation studies in the autoregressive model with orders p show that the proposed procedure is effective.