BIVARIATE SYMMETRICAL STATISTICS OF LONG-RANGE DEPENDENT OBSERVATIONS

被引：21

作者：

DEHLING, H

TAQQU, MS

机构：

[1] STATE UNIV GRONINGEN,DEPT MATH,9700 AV GRONINGEN,NETHERLANDS

[2] BOSTON UNIV,DEPT MATH,BOSTON,MA 02215

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1991年 / 28卷 / 02期

关键词：

VONMISES STATISTICS; U-STATISTICS; GOODNESS OF FIT; CHI-SQUARED TEST; CRAMER-VONMISES-SMIRNOV TEST; MULTIPLE INTEGRATION; HOEFFDING DECOMPOSITION; FRACTIONAL BROWNIAN MOTION; ROSENBLATT PROCESS;

D O I：

10.1016/0378-3758(91)90023-8

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：

Let (X(j))j infinity = 1 be a stationary, mean-zero Gaussian sequence with covariances r(k) = EX(k+1)X1 satisfying r(0) = 1 and r(k) = k-D L(k) where D is small and L is slowly varying at infinity. Consider the sequence Y(j) = G(X(j)), j = 1,2,..., where G is any measurable function. We obtain the asymptotic distribution of certain degenerate von Mises and U-statistics based on the Y(j). As applications, we consider the sample variance, the chi-2-squared goodness of fit test and the Cramer-von Mises-Smirnov omega-2 criterion. The results are non-standard.

引用

页码：153 / 165

页数：13