On the strong convergence forweighted sums of negatively superadditive dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 295-308
Author(s):  
Lulu Zheng ◽  
Xuejun Wang ◽  
Wenzhi Yang
Keyword(s):  
Strong Convergence ◽  
Complete Convergence ◽  
Random Variables ◽  
Maximal Inequality ◽  
Weighted Sums ◽  
Exponential Inequality ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Identical Distribution ◽  
Nsd Random Variables

In this paper, we present some results on the complete convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables by using the Rosenthal-type maximal inequality, Kolmogorov exponential inequality and the truncation method. The results obtained in the paper extend the corresponding ones for weighted sums of negatively associated random variables with identical distribution to the case of arrays of rowwise NSD random variables without identical distribution.

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

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Wenzhi Yang
Keyword(s):  
Complete Convergence ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

Let{Xni,i≥1,n≥1}be an array of rowwise asymptotically almost negatively associated random variables. Some sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables is obtained.

On the Almost sure Convergence Rate for Weighted Sums of Negatively Associated Random Variables with Application to Priestley-Chao Estimate

2015 ◽  
Vol 742 ◽  
pp. 449-452
Author(s):  
Gan Ji Huang ◽  
Guo Dong Xing
Keyword(s):  
Convergence Rate ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Exponential Inequality ◽  
Regression Estimate ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables ◽  
Existing Result

This paper deals with the problem of almost sure convergence rate for weighted sums of negatively associated random variables. A new convergence rate is obtained base on an exponential inequality, the result obtained extends and has a fast convergence rate compare with the existing result. As an application, we study the Priestley-Chao estimate of nonparametric regression estimate and the convergence rate is derived.

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 CONVERGENCE FOR WEIGHTED SUMS OF SEQUENCES OF AANA RANDOM VARIABLES

2008 ◽  
Vol 50 (3) ◽  
pp. 351-357 ◽  
Author(s):  
GUANG-HUI CAI ◽  
BAO-CAI GUO
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Rocky Mountain ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

AbstractLet Xn, n ≥ 1 be an asymptotically almost negatively associated (AANA) sequence of random variables. Some complete convergence and Marcinkiewicz–Zygmund type strong laws of large numbers for an AANA sequence of random variables are obtained. The results obtained generalize the results of Kim, Ko and Lee (Kim, T. S., Ko, M. H. and Lee, I. H. 2004. On the strong laws for asymptotically almost negatively associated random variables. Rocky Mountain J. of Math. 34, 979–989.).

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.

scholarly journals On strong limit theorems for negatively superadditive dependent random variables

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1541-1547
Author(s):  
Yongjun Zhang
Keyword(s):  
Strong Convergence ◽  
Limit Theorems ◽  
Complete Convergence ◽  
Convergence Property ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Limit ◽  
Nsd Random Variables ◽  
Independent Identically Distributed

In this paper, we obtain strong convergence property for Jamison weighted sums of negatively superadditive dependent (NSD, in short) random variables, which extends the famous Jamison theorem. In addition, some sufficient conditions for complete convergence for weighed sums of NSD random variables are presented. These results generalize the corresponding results for independent identically distributed random variables to the case of NSD random variables without assumption of identical distribution.

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