Strong law of large numbers and complete convergence for sequences of φ-mixing random variables

2007 ◽  
Vol 12 (2) ◽  
pp. 211-217 ◽  
Author(s):  
Shixin Gan ◽  
Pingyan Chen ◽  
Dehua Qiu
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Large Numbers ◽  
Mixing Random Variables

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 On Complete Convergence for Weighted Sums ofρ*-Mixing Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Aiting Shen ◽  
Xinghui Wang ◽  
Huayan Zhu
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Large Numbers ◽  
Mixing Random Variables ◽  
Independent And Identically Distributed

We prove the strong law of large numbers for weighted sums∑i=1n‍aniXi, which generalizes and improves the corresponding one for independent and identically distributed random variables andφ-mixing random variables. In addition, we present some results on complete convergence for weighted sums ofρ*-mixing random variables under some suitable conditions, which generalize the corresponding ones for independent random variables.

scholarly journals A Note on the Strong Law of Large Numbers for Arrays of Rowwiseρ˜-Mixing Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Aiting Shen ◽  
Shuhe Hu
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Large Numbers ◽  
Mixing Random Variables

Let{Xni,i≥1,n≥1}be an array of rowwiseρ˜-mixing random variables. Some strong law of large numbers for arrays of rowwiseρ˜-mixing random variables is studied under some simple and weak conditions.

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.

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