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December 2008 The asymptotic distribution and Berry–Esseen bound of a new test for independence in high dimension with an application to stochastic optimization
Wei-Dong Liu, Zhengyan Lin, Qi-Man Shao
Ann. Appl. Probab. 18(6): 2337-2366 (December 2008). DOI: 10.1214/08-AAP527

Abstract

Let X1, …, Xn be a random sample from a p-dimensional population distribution. Assume that c1nαpc2nα for some positive constants c1, c2 and α. In this paper we introduce a new statistic for testing independence of the p-variates of the population and prove that the limiting distribution is the extreme distribution of type I with a rate of convergence $O((\log n)^{5/2}/\sqrt{n})$. This is much faster than O(1/log n), a typical convergence rate for this type of extreme distribution. A simulation study and application to stochastic optimization are discussed.

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Wei-Dong Liu. Zhengyan Lin. Qi-Man Shao. "The asymptotic distribution and Berry–Esseen bound of a new test for independence in high dimension with an application to stochastic optimization." Ann. Appl. Probab. 18 (6) 2337 - 2366, December 2008. https://doi.org/10.1214/08-AAP527

Information

Published: December 2008
First available in Project Euclid: 26 November 2008

zbMATH: 1154.60021
MathSciNet: MR2474539
Digital Object Identifier: 10.1214/08-AAP527

Subjects:
Primary: 60F05
Secondary: 62F05

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 6 • December 2008
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