A Note on the ASCLT for Triangular Arrays of Random Variables with an Extension to U-statistics

被引：0

作者：

Zhang, Yong ^{[1
]}

Yang, Xiao Yun ^{[1
]}

机构：

[1] Jilin Univ, Coll Math, Changchun 130012, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2012年 / 28卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Almost sure central limit theorem; triangular arrays; products of sums; U-statistics; CENTRAL-LIMIT-THEOREM; INDEPENDENT SUMS; PRODUCTS; ASYMPTOTICS;

D O I：

10.1007/s10114-012-9241-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we obtain an almost sure central limit theorem for products of independent sums of positive random variables. An extension of the result gives an ASCLT for the U-statistics.

引用

页码：1907 / 1916

页数：10

共 13 条

[1] Billingsley P., 1968, CONVERGE PROBAB MEAS
[2] AN ALMOST EVERYWHERE CENTRAL LIMIT-THEOREM
BROSAMLER, GA
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1988, 104 : 561 - 574
[3] A note on the almost sure limit theorem for the product of partial sums
Gonchigdanzan, K
Rempala, GA
[J]. APPLIED MATHEMATICS LETTERS, 2006, 19 (02) : 191 - 196
[4] A CLASS OF STATISTICS WITH ASYMPTOTICALLY NORMAL DISTRIBUTION
HOEFFDING, W
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1948, 19 (03): : 293 - 325
[5] Asymptotics for sums of a function of normalized independent sums
Kosinski, Kamil
[J]. STATISTICS & PROBABILITY LETTERS, 2009, 79 (04) : 415 - 419
[6] Lee A. J., 1990, U STAT STAT TXB MONO, V110
[7] A note on asymptotic distribution of products of sums
Lu, XW
Qi, YC
[J]. STATISTICS & PROBABILITY LETTERS, 2004, 68 (04) : 407 - 413
[8] A NOTE ON THE ALMOST SURE CENTRAL-LIMIT-THEOREM FOR WEAKLY DEPENDENT RANDOM-VARIABLES
PELIGRAD, M
SHAO, QM
[J]. STATISTICS & PROBABILITY LETTERS, 1995, 22 (02) : 131 - 136
[9] Limit distributions for products of sums
Qi, YC
[J]. STATISTICS & PROBABILITY LETTERS, 2003, 62 (01) : 93 - 100
[10] Asymptotics for products of independent sums with an application to Wishart determinants
Rempala, G
Wesolowski, J
[J]. STATISTICS & PROBABILITY LETTERS, 2005, 74 (02) : 129 - 138

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