Marcinkiewicz-Zygmund strong laws for U-statistics of weakly dependent observations

被引：6
|
作者：
Dehling, Herold G. [1 ]
Sharipov, Olimjon Sh. [2 ]
机构：
[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany
[2] Uzbek Acad Sci, Inst Math & Informat Technol, Dept Probabil Theory & Math Stat, Tashkent 100125, Uzbekistan
来源：
STATISTICS & PROBABILITY LETTERS | 2009年 / 79卷 / 19期
关键词：
LIMITING BEHAVIOR; CONVERGENCE;
D O I：
10.1016/j.spl.2009.06.012
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：
We prove the Marcinkiewicz-Zygmund Strong Law of Large Numbers for U-statistics of strictly stationary, absolutely regular observations (xi(i))(i >= 1).Under suitable moment conditions and conditions on the mixing rate, we show that n(-2+gamma) Sigma(1 <= i<j <= n) (h(xi(i), xi(j)) - Eh(xi, eta)) -> 0 for some gamma >= 0, in the non-degenerate case, and n(-1+gamma) Sigma(1 <= i<j <= n) (h(xi(i), xi(j)) - Eh(xi, eta)) -> 0 in the degenerate case. (C) 2009 Elsevier B.V. All rights reserved.
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页码：2028 / 2036
页数：9
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