Bahadur Representation for Quantiles of Empirical DF's of Generalized U-Statistic Structure

摘要

A wide class of c-sample statistics can be represented conveniently as quantiles of a nonclassical empirical df having the structure of a generalized U-statistic. A key tool in studying classical quantiles has been the Bahadur representation. This paper provides a suitable extension of that tool to the generalized setting. As auxiliary lemmas, some new results for generalized U-statistics are developed. Also, some further results for empirical df's of generalized U-statistic structure and their corresponding quantiles are provided. Keywords: Empirical distributions; Nonparametric estimation, and Probability inequalities. (Author)