Strong limit theorems for weighted sums of negatively associated random variables

Bing Yi Jing; Han Ying Liang

doi:10.1007/s10959-007-0128-4

Strong limit theorems for weighted sums of negatively associated random variables

Bing Yi Jing, Han Ying Liang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal Article › peer-review

49 Citations (Scopus)

Abstract

In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables. Marcinkiewicz-Zygmund's strong law of large numbers is extended to weighted sums of negatively associated random variables. Furthermore, we investigate various limit properties of Cesàro's and Riesz's sums of negatively associated random variables. Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409-412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105-112, 2000), Li et al. (J. Theor. Probab. 8, 49-76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169-178, 1993) are also improved and extended to the negatively associated setting.

Original language	English
Pages (from-to)	890-909
Number of pages	20
Journal	Journal of Theoretical Probability
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s10959-007-0128-4
Publication status	Published - Dec 2008

Keywords

Cesàro mean
Complete convergence
Negatively associated random variable
Strong law
Weighted sum

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10.1007/s10959-007-0128-4

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title = "Strong limit theorems for weighted sums of negatively associated random variables",

abstract = "In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables. Marcinkiewicz-Zygmund's strong law of large numbers is extended to weighted sums of negatively associated random variables. Furthermore, we investigate various limit properties of Ces{\`a}ro's and Riesz's sums of negatively associated random variables. Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409-412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105-112, 2000), Li et al. (J. Theor. Probab. 8, 49-76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169-178, 1993) are also improved and extended to the negatively associated setting.",

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TY - JOUR

T1 - Strong limit theorems for weighted sums of negatively associated random variables

AU - Jing, Bing Yi

AU - Liang, Han Ying

PY - 2008/12

Y1 - 2008/12

N2 - In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables. Marcinkiewicz-Zygmund's strong law of large numbers is extended to weighted sums of negatively associated random variables. Furthermore, we investigate various limit properties of Cesàro's and Riesz's sums of negatively associated random variables. Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409-412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105-112, 2000), Li et al. (J. Theor. Probab. 8, 49-76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169-178, 1993) are also improved and extended to the negatively associated setting.

AB - In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables. Marcinkiewicz-Zygmund's strong law of large numbers is extended to weighted sums of negatively associated random variables. Furthermore, we investigate various limit properties of Cesàro's and Riesz's sums of negatively associated random variables. Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409-412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105-112, 2000), Li et al. (J. Theor. Probab. 8, 49-76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169-178, 1993) are also improved and extended to the negatively associated setting.

KW - Cesàro mean

KW - Complete convergence

KW - Negatively associated random variable

KW - Strong law

KW - Weighted sum

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UR - https://openalex.org/W2061197393

UR - https://www.scopus.com/pages/publications/54149107044

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DO - 10.1007/s10959-007-0128-4

M3 - Journal Article

SN - 0894-9840

VL - 21

SP - 890

EP - 909

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 4

ER -

Strong limit theorems for weighted sums of negatively associated random variables

Abstract

Keywords

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