scholarly journals Complete convergence for weighted sums of a class of random variables

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 509-522 ◽  
Author(s):  
Xin Deng ◽  
Meimei Ge ◽  
Xuejun Wang ◽  
Yanfang Liu ◽  
Yu Zhou
Keyword(s):  
Complete Convergence ◽  
Type Inequality ◽  
Random Variables ◽  
Random Variable ◽  
Weighted Sums ◽  
Real Numbers ◽  
Mild Conditions ◽  
Rosenthal Type Inequality

Let {ani,1?i?n,n?1} be an array of real numbers and {Xn,n?1} be a sequence of random variables satisfying the Rosenthal type inequality, which is stochastically dominated by a random variable X. Under mild conditions, we present some results on complete convergence for weighted sums ?ni=1 aniXi of random variables satisfying the Rosenthal type inequality. The results obtained in the paper generalize some known ones in the literatures.

scholarly journals Complete moment convergence of moving average processes for m-WOD sequence

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lihong Guan ◽  
Yushan Xiao ◽  
Yanan Zhao
Keyword(s):  
Moving Average ◽  
Random Variables ◽  
Random Variable ◽  
Complete Moment Convergence ◽  
Real Numbers ◽  
Mild Conditions ◽  
Moment Convergence ◽  
Summable Sequence ◽  
Moving Average Processes ◽  
Widely Orthant Dependent

AbstractIn this paper, the complete moment convergence for the partial sum of moving average processes $\{X_{n}=\sum_{i=-\infty }^{\infty }a_{i}Y_{i+n},n\geq 1\}$ { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } is established under some mild conditions, where $\{Y_{i},-\infty < i<\infty \}$ { Y i , − ∞ < i < ∞ } is a sequence of m-widely orthant dependent (m-WOD, for short) random variables which is stochastically dominated by a random variable Y, and $\{a_{i},-\infty < i<\infty \}$ { a i , − ∞ < i < ∞ } is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results from m-extended negatively dependent (m-END, for short) sequences to m-WOD sequences.

Complete convergence and complete moment convergence for extended negatively dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1381-1394 ◽  
Author(s):  
Aiting Shen ◽  
Yu. Zhang ◽  
Wenjuan Wang
Keyword(s):  
Complete Convergence ◽  
Type Inequality ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Moment Inequalities ◽  
Dependent Random Variables ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables ◽  
End Random Variables

In this paper, we provide some probability and moment inequalities (especially the Marcinkiewicz-Zygmund type inequality) for extended negatively dependent (END, in short) random variables. By using the Marcinkiewicz-Zygmund type inequality and the truncation method, we investigate the complete convergence for sums and weighted sums of arrays of rowwise END random variables. In addition, the complete moment convergence for END random variables is obtained. Our results generalize and improve the corresponding ones of Wang et al. [18] and Baek and Park [2].

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 The law of iterated logarithm for a class of random variables satisfying Rosenthal type inequality

2021 ◽  
Vol 6 (10) ◽  
pp. 11076-11083
Author(s):  
Haichao Yu ◽  
◽  
Yong Zhang
Keyword(s):  
Type Inequality ◽  
Random Variables ◽  
Random Variable ◽  
Law Of Iterated Logarithm ◽  
Variable Sequence ◽  
Iterated Logarithm ◽  
Rosenthal Type Inequality ◽  
The Law

<abstract><p>Let $ \{Y_n, n\geq 1\} $ be sequence of random variables with $ EY_n = 0 $ and $ \sup_nE|Y_n|^p &lt; \infty $ for each $ p &gt; 2 $ satisfying Rosenthal type inequality. In this paper, the law of the iterated logarithm for a class of random variable sequence with non-identical distributions is established by the Rosenthal type inequality and Berry-Esseen bounds. The results extend the known ones from i.i.d and NA cases to a class of random variable satisfying Rosenthal type inequality.</p></abstract>

scholarly journals Complete convergence for weighted sums of pairwise independent random variables

2017 ◽  
Vol 15 (1) ◽  
pp. 467-476
Author(s):  
Li Ge ◽  
Sanyang Liu ◽  
Yu Miao
Keyword(s):  
Rate Of Convergence ◽  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Pairwise Independent Random Variables ◽  
Moving Average Processes

Abstract In the present paper, we have established the complete convergence for weighted sums of pairwise independent random variables, from which the rate of convergence of moving average processes is deduced.

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