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Stein's method for negatively associated random variables with applications to second-order stationary random fields

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  28 March 2018

Nathakhun Wiroonsri
Nathakhun Wiroonsri*
Affiliation:
University of Southern California
*
* Postal address: Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA. Email address: wiroonsr@usc.edu
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Abstract

Let ξ = (ξ1, . . ., ξm) be a negatively associated mean-zero random vector with components that obey the bound |ξi| ≤ B, i = 1, . . ., m, and whose sum W = ∑i=1mξi has variance 1. The bound d1(ℒ(W), ℒ(Z)) ≤ 5B - 5.2∑i≠ jσij is obtained, where Z has the standard normal distribution and d1(∙, ∙) is the L1 metric. The result is extended to the multidimensional case with the L1 metric replaced by a smooth functions metric. Applications to second-order stationary random fields with exponential decreasing covariance are also presented.

Keywords

Correlation inequalityblock dependencenegative dependencerandom field

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G60: Random fields
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 196 - 215
Copyright
Copyright © Applied Probability Trust 2018 

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