Laws of the iterated logarithm for the local U-statistic process

被引：27

作者：

Gine, Evarist

Mason, David M.

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Univ Delaware, Newark, DE 19717 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2007年 / 20卷 / 03期

基金：

美国国家科学基金会;

关键词：

U-statistics; law of iterated logarithm; empirical process; kernel density estimation; SMOOTHED EMPIRICAL PROCESSES; LIMIT-THEOREMS; UNIFORM CONSISTENCY; FUNCTION ESTIMATORS; DENSITY ESTIMATORS; WEAK-CONVERGENCE; RANDOM-VARIABLES;

D O I：

10.1007/s10959-007-0067-0

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Laws of the iterated logarithm are established for the local U-statistic process. This entails the development of probability inequalities and moment bounds for U-processes that should be of separate interest. The local U-statistic process is based upon an estimator of the density of a function of several i.i.d. variables proposed by Frees (J. Am. Stat. Assoc. 89, 517-525, 1994). As a consequence, our results are directly applicable to the derivation of exact rates of uniform in bandwidth consistency in the sup and in the L-p norms for these estimators.

引用

页码：457 / 485

页数：29

共 30 条

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