Equivalent conditions of complete convergence for m-dimensional products of iid random variables and application to strong law of large numbers

2000 ◽  
Vol 43 (11) ◽  
pp. 1144-1153
Author(s):  
Yuebao Wang ◽  
Chun Su ◽  
Hanying Liang ◽  
Fengyang Cheng
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Large Numbers ◽  
Equivalent Conditions

scholarly journals Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums ofρ~-Mixing Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chongfeng Lan
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Large Numbers ◽  
Sufficient And Necessary Conditions ◽  
Complete Convergence Theorem ◽  
Mixing Random Variables ◽  
Equivalent Conditions

The equivalent conditions of complete convergence are established for weighted sums ofρ~-mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence ofρ~-mixing random variables is obtained.

scholarly journals Complete Convergence of the Maximum Partial Sums for Arrays of Rowwise of AANA Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Aiting Shen ◽  
Ranchao Wu ◽  
Yan Chen ◽  
Yu Zhou
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Positive Real ◽  
Strong Law ◽  
Limiting Behavior ◽  
Large Numbers ◽  
Rowwise Independent

The limiting behavior of the maximum partial sums(1/an)max1≤j≤n|∑i=1j‍Xni|is investigated, and some new results are obtained, where{Xni,i≥1,n≥1}is an array of rowwise AANA random variables and{an,n≥1}is a sequence of positive real numbers. As an application, the Chung-type strong law of large numbers for arrays of rowwise AANA random variables is obtained. The results extend and improve the corresponding ones of Hu and Taylor (1997) for arrays of rowwise independent random variables.

scholarly journals Complete convergence for weighted sums of widely orthant-dependent random variables

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pingyan Chen ◽  
Soo Hak Sung
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Link Type ◽  
Convergence Results ◽  
Large Numbers ◽  
Widely Orthant Dependent

AbstractThe complete convergence results for weighted sums of widely orthant-dependent random variables are obtained. A strong law of large numbers for weighted sums of widely orthant-dependent random variables is also obtained. Our results extend and generalize some results of Chen and Sung (J. Inequal. Appl. 2018:121, 2018), Zhang et al. (J. Math. Inequal. 12:1063–1074, 2018), Chen and Sung (Stat. Probab. Lett. 154:108544, 2019), Lang et al. (Rev. Mat. Complut., 2020, 10.1007/s13163-020-00369-5), and Liang (Stat. Probab. Lett. 48:317–325, 2000).

On complete convergence for weighted sums of arrays of rowwise END random variables and its statistical applications

2019 ◽  
Vol 69 (1) ◽  
pp. 223-232
Author(s):  
Xiaohan Bao ◽  
Junjie Lin ◽  
Xuejun Wang ◽  
Yi Wu
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Nonparametric Regression Model ◽  
Strong Law ◽  
Mild Conditions ◽  
Large Numbers ◽  
End Random Variables

Abstract In this paper, the complete convergence for the weighted sums of arrays of rowwise extended negatively dependent (END, for short) random variables is established under some mild conditions. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for arrays of rowwise END random variables is also obtained. The result obtained in the paper generalizes and improves some corresponding ones for independent random variables and some dependent random variables in some extent. By using the complete convergence that we established, we further study the complete consistency for the weighted estimator in a nonparametric regression model based on END errors.

scholarly journals On Strong Convergence for Weighted Sums of a Class of Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Aiting Shen
Keyword(s):  
Strong Convergence ◽  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Maximal Inequality ◽  
Weighted Sums ◽  
Moment Condition ◽  
Strong Law ◽  
Linear Statistics ◽  
Large Numbers

Let{Xn,n≥1}be a sequence of random variables satisfying the Rosenthal-type maximal inequality. Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition. As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained. Our result generalizes the corresponding one of Zhou et al. (2011) and improves the corresponding one of Wang et al. (2011, 2012).

scholarly journals Complete moment convergence for weighted sums of negatively orthant dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1195-1206 ◽  
Author(s):  
Xuejun Wang ◽  
Zhiyong Chen ◽  
Ru Xiao ◽  
Xiujuan Xie
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Strong Law ◽  
Associated Random Variables ◽  
Moment Convergence ◽  
Large Numbers

In this paper, the complete moment convergence and the integrability of the supremum for weighted sums of negatively orthant dependent (NOD, in short) random variables are presented. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for NODrandom variables are obtained. The results established in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.

scholarly journals On Complete Convergence of Weighted Sums for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Wenzhi Yang ◽  
Xinghui Wang
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Type Result ◽  
Strong Law ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

Let{Xni,i≥1,n≥1}be an array of rowwise asymptotically almost negatively associated (AANA, in short) random variables. The complete convergence for weighted sums of arrays of rowwise AANA random variables is studied, which complements and improves the corresponding result of Baek et al. (2008). As applications, the Baum and Katz type result for arrays of rowwise AANA random variables and the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of AANA random variables are obtained.

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