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arXiv · 0901.2468

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
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Abstract

Let $\mathbf{X}_1,...,\mathbf{X}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1n^α\leq p\leq c_2n^α$ for some positive constants $c_1,c_2$ 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. 2009-01-16. The asymptotic distribution and Berry--Esseen bound of a new test for independence in high dimension with an application to stochastic optimization. https://doi.org/10.1214/08-aap527

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