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The asymptotic distribution and Berry–Esseen bound of a new test for independence in high dimension with an application to stochastic optimization
2008
The Annals of Applied Probability
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Let X_1,...,X_n be a random sample from a p-dimensional population distribution. Assume that c_1n^α≤ p≤ 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(( n)^5/2/√(n)). This is much faster than O(1/ n), a typical convergence rate for this type of extreme distribution. A simulation
doi:10.1214/08-aap527
fatcat:amyip73mjrgjne45wmlnhi7nwa