MAXIMAL INEQUALITIES FOR DEGENERATE U-PROCESSES WITH APPLICATIONS TO OPTIMIZATION ESTIMATORS
成果类型：
Article
署名作者：
SHERMAN, RP
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176325377
发表日期：
1994
页码：
439-459
关键词：
摘要：
Maximal inequalities for degenerate U-processes of order k, k greater-than-or-equal-to 1, are established. The results rest on a moment inequality (due to Bonami) for kth-order forms and on extensions of chaining and symmetrization inequalities from the theory of empirical processes. Rates of uniform convergence are obtained. The maximal inequalities can be used to determine the limiting distribution of estimators that optimize criterion functions having U-process structure. As an application, a semiparametric regression estimator that maximizes a U-process of order 3 is shown to be square-root n-consistent and asymptotically normally distributed.