A note on the exponential inequality for associated random variables

2007 ◽  
Vol 77 (18) ◽  
pp. 1730-1736 ◽  
Author(s):  
Soo Hak Sung
Keyword(s):  
Random Variables ◽  
Exponential Inequality ◽  
Associated Random Variables

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.

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.

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