Smallest nonparametric tolerance regions

• 成果类型: Article
• 署名作者: Di Bucchianico, A; Einmahl, JHJ; Mushkudiani, NA
• 署名单位: Eindhoven University of Technology; Eindhoven University of Technology; Tilburg University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 1320-1343
• 关键词: generalized quantile processes; data depth; minimum

摘要

We present a new, natural way to construct nonparametric multivariate tolerance regions. Unlike the classical nonparametric tolerance intervals, where the endpoints are determined by beforehand chosen order statistics, we take the shortest interval, that contains a certain number of observations. We extend this idea to higher dimensions by replacing the class of intervals by a general class of indexing sets, which specializes to the classes of ellipsoids, hyperrectangles or convex sets. The asymptotic behavior of our tolerance regions is derived using empirical process theory, in particular the concept of generalized quantiles. Finite sample properties of our tolerance regions are investigated through a simulation study. Real data examples are also presented.