An Exponential Inequality for Symmetric Random Variables

2015 ◽  
Vol 122 (8) ◽  
pp. 786
Author(s):  
Raphaël Cerf ◽  
Matthias Gorny
Keyword(s):  
Random Variables ◽  
Exponential Inequality

scholarly journals On the Exponential Inequality for Weighted Sums of a Class of Linearly Negative Quadrant Dependent Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Guodong Xing ◽  
Shanchao Yang
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Exponential Inequality ◽  
Precise Asymptotics ◽  
Dependent Random Variables

The exponential inequality for weighted sums of a class of linearly negative quadrant dependent random variables is established, which extends and improves the corresponding ones obtained by Ko et al. (2007) and Jabbari et al. (2009). In addition, we also give the relevant precise asymptotics.

A note on the exponential inequality for a class of dependent random variables

2011 ◽  
Vol 40 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Soo Hak Sung ◽  
Patchanok Srisuradetchai ◽  
Andrei Volodin
Keyword(s):  
Random Variables ◽  
Exponential Inequality ◽  
Dependent 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.

scholarly journals Moment inequality of the minimum for nonnegative negatively orthant dependent random variables

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1475-1481
Author(s):  
Xuejun Wang ◽  
Shijie Wang ◽  
Shuhe Hu
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Exponential Inequality ◽  
Moment Inequalities ◽  
Moment Inequality ◽  
Dependent Random Variables ◽  
The Moment

Let {xn,n ? 1} be a sequence of positive numbers and {?n,n ? 1} be a sequence of nonnegative negatively orthant dependent (NOD) random variables satisfying certain distribution conditions. An exponential inequality for the minimum min1?i?n xi?i is given. In addition, the moment inequalities of the minimum (Ek - min1?i?n|xi?i|p)1/p for nonnegative negatively orthant dependent random variables are established, where p > 0 and k = 1,2,..., n. Our results generalize the corresponding ones for independent random variables to the case of negatively orthant dependent random variables.

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