The Asymptotic Distribution and Berry–esseen Bound of a New Test for Independence in High Dimension with an Application to Stochastic Optimization

@inproceedings{Liu2009TheAD,
  title={The Asymptotic Distribution and Berry–esseen Bound of a New Test for Independence in High Dimension with an Application to Stochastic Optimization},
  author={Wei-dong Liu and Zhengyan Lin and Qi-Man Shao},
  year={2009}
}
Let X1, . . . ,Xn be a random sample from a p-dimensional population distribution. Assume that c1n α ≤ p ≤ c2n 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((logn)/ √ n). This is much faster than O(1/ log n), a typical convergence rate for this type of extreme distribution. A simulation… CONTINUE READING

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