Distribution-free tests of independence in high dimensions

Fang Han, Shizhe Chen and Han Liu

Biometrika, 2017, vol. 104, issue 4, 813-828

Abstract: SummaryWe consider the testing of mutual independence among all entries in a $d$-dimensional random vector based on $n$ independent observations. We study two families of distribution-free test statistics, which include Kendall’s tau and Spearman’s rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and we propose tests that control the Type I error in the high-dimensional setting where $d >n$. We further show that the two tests are rate-optimal in terms of power against sparse alternatives and that they outperform competitors in simulations, especially when $d$ is large.

Keywords: Gumbel distribution; Kendall’s tau; Linear rank statistic; Mutual independence; Rank-type U-statistic; Spearman’s rho (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (9)

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