文章基本信息

标题：Multivariate Location: Robust Estimators And Inference
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作者：Wilcox, Rand R. ; Keselman, H. J.
期刊名称：Journal of Modern Applied Statistical Methods
出版年度：2004
卷号：3
期号：1
页码：2
出版社：Wayne State University
摘要：The sample mean can have poor efficiency relative to various alternative estimators under arbitrarily small departures from normality. In the multivariate case, (affine equivariant) estimators have been proposed for dealing with this problem, but a comparison of various estimators by Massé and Plante (2003) indicated that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the skipped estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal distributions.
关键词：Outlier detection; Tukey’s halfspace depth; skipped estimators; outlier-projection estimator