A limit result for U-statistics of binary variables

被引：1

作者：

Utev, S ^{[1
]}

Becker, NG ^{[1
]}

机构：

[1] La Trobe Univ, Sch Stat Sci, Bundoora, Vic 3083, Australia

来源：

JOURNAL OF THEORETICAL PROBABILITY | 1998年 / 11卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

U-type statistics; binary random variables; law of the iterated logarithm;

D O I：

10.1023/A:1022666901529

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：

Define r/(k, n) = U-k,U- n - n(k/2)H(k)(Sigma(j =1)(n) X-j/root n), where U-k,U- n = Sigma(1) less than or equal to i(1) not equal ... not equal i(k) less than or equal to n X-i1...X-ik is a symmetric U-type statistic, H-k(.) is the Hermite polynomial of degree k, and {X, X-n, n greater than or equal to 1} are independent identically distributed binary random variables with Pr(X is an element of {-1, 1}) = 1. We show that [GRAPHICS] according as EX = 0 or EX not equal 0, respectively.

引用

页码：853 / 856

页数：4

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