On the Maximal Inequalities for Partial Sums of Strong Mixing Random Variables with Applications

被引：0

作者：

Xing, Guo-dong ^{[1
]}

Yang, Shan-chao ^{[2
]}

机构：

[1] Hunan Univ Sci & Engn, Dept Math, Yongzhou 425100, Hunan, Peoples R China

[2] Guangxi Normal Univ, Dept Math, Guilin, Guangxi, Peoples R China

来源：

THAI JOURNAL OF MATHEMATICS | 2011年 / 9卷 / 01期

关键词：

Convergence rate; Gasser-Muller estimator; Maximal inequality; Strong mixing;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Maximal inequalities for partial sums of strong mixing random variables are established. To show the applications of the inequalities obtained, we discuss the strong consistency of Gasser-Muller estimator of fixed design regression estimate and obtain the almost sure convergence rate n (1/2)(log log n) (1/xi) log(3/2) n with any 0 < xi < 2, which closes to the optimal achievable convergence rate for independent random variables under an iterated logarithm.

引用

页码：11 / 19

页数：9

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