Concentration inequalities for dependent random variables

... inequality for sampling without replacement 288 xii Summary This thesis contains contributions to the theory of concentration inequalities, in particular, concentration inequalities for dependent random ... (including the case of dependent random variables satisfying the Dobrushin condition), and locally dependent random variables In each of these cases, we prove ne...

Ngày tải lên: 09/09/2015, 11:06

... generalizes and improves the corresponding results of Yang [9] for NA random variables and Wang et al [10] for NOD random variables In Section 3, we will study the complete convergence for acceptable random ... acceptable random variables generalizes and improves the corresponding results presented by Yang for NA random variables and Wang et al for NO...

Ngày tải lên: 18/06/2014, 15:20

... generalizes and improves the corresponding results of Yang [9] for NA random variables and Wang et al [10] for NOD random variables In Section 3, we will study the complete convergence for acceptable random ... variables using the exponential inequalities established in Section 2 Exponential inequalities for acceptable random variables In this section...

Ngày tải lên: 20/06/2014, 23:20

... is to study the strong limit theorems for arrays of rowwise NOD random variables As an application, the Chung-type strong law of large numbers for arrays of rowwise NOD random variables is obtained ... consider the strong law of large numbers for arrays of rowwise negatively associated (NA) random variables A finite collection of random...

Ngày tải lên: 20/06/2014, 22:20

... independent random variables have been extended to dependent random variables by many authors The concept of negatively associated random variables was introduced by Alam and Saxena [6] and carefully ... complete convergence theorems for negatively associated and negatively dependent mean zero random variables The following lemma is an exponential inequality for nega...

Ngày tải lên: 20/06/2014, 22:20

... negatively dependent random variables,” Pakistan Journal of Statistics, vol 21, no 3, pp 257–264, 2005 H R Nili Sani, M Amini, and A Bozorgnia, Strong laws for weighted sums of negative dependent random ... Netherlands, 1996 M Amini, Some contribution to limit theorems for negatively dependent random variable, Ph.D thesis, 2000 V Fakoor and H A Azarnoosh, “P...

Ngày tải lên: 21/06/2014, 07:20

... 2005 S.-C Yang and M Chen, Exponential inequalities for associated random variables and strong laws of large numbers,” Science in China A, vol 50, no 5, pp 705–714, 2006 I Dewan and B L S Prakasa ... inequality for associated random variables, ” Statistics & Probability Letters, vol 42, no 4, pp 423–431, 1999 Guodong Xing et al 11 P E Oliveira, “An exponential inequ...

Ngày tải lên: 21/06/2014, 22:20

... Type Inequalities for CDFs An Inequality of the Ostrowski Type for CDFs Random Variables whose PDFs Belong to L∞ [a, b] Random Variables whose PDFs Belong to Lp [a, b] , p > Better Bounds for ... Elementary Inequalities for the Variance Elementary Inequalities Perturbed Inequalities Further Inequalities for Univariate Moments 185 185 200 219 iii iv CONTENTS Chapter...

Ngày tải lên: 20/07/2014, 18:38

... A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law Qunying Wu1,2 College of Science, Guilin University ... establish the ASCLT for self-normalized partial sums of random variables in the domain of attraction of the normal law,...

Ngày tải lên: 20/06/2014, 21:20

... variable sequences and NA random variable sequences are the most important and special cases of pairwise NQD random variable sequences, then we have the following results as two corollaries of ... this article as: Huang et al.: A note on the complete convergence for sequences of pairwise NQD random variables Journal of Inequalities and Applicatio...

Ngày tải lên: 20/06/2014, 22:20

... almost sure central limit theorem for the product of partial sums, ” Applied Mathematics Letters, vol 19, pp 191–196, 2004 J S Jin, “An almost sure central limit theorem for the product of partial sums ... Utev, Central limit theorem for linear processes,” The Annals of Probability, vol 25, no 1, pp 443–456, 1997 F Jonsson, Almost Sure Cent...

Ngày tải lên: 21/06/2014, 05:20

... On complete convergence for arrays of rowwise dependent random variables, ” Statistics & Probability Letters, vol 77, no 11, pp 1050–1060, 2007 17 A Kuczmaszewska, On complete convergence for ... arrays of negatively dependent random variables and its applications,” Journal of Theoretical Probability, vol 23, no 2, pp 362–377, 2010 19 S H Sung, Complete...

Ngày tải lên: 21/06/2014, 07:20

... tighter Gruss-type ¨ bound for the covariance of two transformed random variables by incorporating a notion of quadrant dependence and also utilizing the idea of constraining the means of the random ... when C x, y ≤ for all x and y, then the random variables are negatively quadrant dependent For applications of these notions of dependence and also...

Ngày tải lên: 21/06/2014, 18:20

... Sung , Xing and Yang , and Xing et al On the other hand, Kim and Kim 10 , Nooghabi and Azarnoosh 11 , and Xing et al 12 obtained exponential inequalities for negatively associated random variables ... Ioannides and G G Roussas, Exponential inequality for associated random variables,” Statistics & Probability Letters, vol 42, no 4, pp 423–431, 1999 P E Oliveira, An exponen...

Ngày tải lên: 21/06/2014, 20:20

... are proved for nonmonotonic functions of associated random variables in Section As an application, a strong law of large numbers is derived for nonmonotonic functions of associated random variables ... proves the strong law of large numbers for nonmonotonic functions of associated random variables Corollary 4.2 Let {Yn , n ≥ 1} be sequence of nonmono...

Ngày tải lên: 22/06/2014, 22:20