Let X1, …, Xn be a random sample from a p-dimensional population distribution. Assume that c1nα≤p≤c2nα 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.
@article{1227708921,
author = {Liu, Wei-Dong and Lin, Zhengyan and Shao, Qi-Man},
title = {The asymptotic distribution and Berry--Esseen bound of a new test for independence in high dimension with an application to stochastic optimization},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 2337-2366},
language = {en},
url = {http://dml.mathdoc.fr/item/1227708921}
}
Liu, Wei-Dong; Lin, Zhengyan; Shao, Qi-Man. 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., Tome 18 (2008) no. 1, pp. 2337-2366. http://gdmltest.u-ga.fr/item/1227708921/