文章基本信息

标题：Note on Qualitative Robustness of Multivariate Sample Mean and Median
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作者：Evgueni Gordienko ; Andrey Novikov ; J. Ruiz de Chávez 等
期刊名称：Journal of Probability and Statistics
印刷版ISSN：1687-952X
电子版ISSN：1687-9538
出版年度：2013
卷号：2013
DOI：10.1155/2013/208950
出版社：Hindawi Publishing Corporation
摘要：It is known that the robustness properties of estimators depend on the choice of a metric in the space of distributions. We introduce a version of Hampel's qualitative robustness that takes into account the -asymptotic normality of estimators in , and examine such robustness of two standard location estimators in . For this purpose, we use certain combination of the Kantorovich and Zolotarev metrics rather than the usual Prokhorov type metric. This choice of the metric is explained by an intention to expose a (theoretical) situation where the robustness properties of sample mean and -sample median are in reverse to the usual ones. Using the mentioned probability metrics we show the qualitative robustness of the sample multivariate mean and prove the inequality which provides a quantitative measure of robustness. On the other hand, we show that -sample median could not be “qualitatively robust” with respect to the same distance between the distributions.