Limiting behavior of weighted sums of i.i.d. random variables

被引：43

作者：

Pingyan, Chen ^{[1
]}

Shixin, Gan ^{[2
]}

机构：

[1] Jinan Univ, Dept Math, Guangzhou 510630, Peoples R China

[2] Wuhan Univ, Coll Math & Stat, Wuhan 430072, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2007年 / 77卷 / 16期

基金：

中国国家自然科学基金;

关键词：

strong laws of large numbers; Chover's LIL; laws of the single logarithm; weighted sums of i.i.d. random variables; Hoffmann-Jorgensen's inequality; rates of convergence in the invariance principle;

D O I：

10.1016/j.spl.2007.03.038

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：

The strong laws of large numbers, Chover's laws of the iterated logarithm (LIL) and laws of the single logarithm are established for weighted sums of i.i.d. random variables under suitable conditions on both the weights and the distribution. (c) 2007 Elsevier B.V. All rights reserved,

引用

页码：1589 / 1599

页数：11

共 28 条

[1] On the strong convergence of weighted sums [J].

Antonini, RG ;

Kwon, JS ;

Sung, SH ;

Volodin, AI .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2001, 19 (06) :903-909

[2]

Bai ZD, 1997, STAT SINICA, V7, P923

[3] Marcinkiewicz strong laws for linear statistics [J].

Bai, ZD ;

Cheng, PE .

STATISTICS & PROBABILITY LETTERS, 2000, 46 (02) :105-112

[4]

Chen P., 2004, SANKHYA, V66, P49

[5]

Chen PY, 2002, STAT PROBABIL LETT, V60, P367

[6]

Chen XB, 2003, SPECTROSC SPECT ANAL, V23, P1

[7] ALMOST SURE CONVERGENCE THEOREMS OF WEIGHTED SUMS OF RANDOM-VARIABLES [J].

CHOI, BD ;

SUNG, SH .

STOCHASTIC ANALYSIS AND APPLICATIONS, 1987, 5 (04) :365-377

[8] A LAW OF ITERATED LOGARITHM FOR STABLE SUMMANDS [J].

CHOVER, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 17 (02) :441-&

[9]

Csörgö M, 2003, ANN PROBAB, V31, P1228

[10] A strong law for weighted sums of IID random variables [J].

Cuzick, J .

JOURNAL OF THEORETICAL PROBABILITY, 1995, 8 (03) :625-641

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