The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 6 (2008), 2337-2366.
The asymptotic distribution and Berry–Esseen bound of a new test for independence in high dimension with an application to stochastic optimization
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 . 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.
Ann. Appl. Probab., Volume 18, Number 6 (2008), 2337-2366.
First available in Project Euclid: 26 November 2008
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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. 18 (2008), no. 6, 2337--2366. doi:10.1214/08-AAP527. https://projecteuclid.org/euclid.aoap/1227708921