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February 2019 Asymptotic power of Rao’s score test for independence in high dimensions
Dennis Leung, Qiman Shao
Bernoulli 25(1): 241-263 (February 2019). DOI: 10.3150/17-BEJ985

Abstract

Let $\mathbf{R}$ be the Pearson correlation matrix of $m$ normal random variables. The Rao’s score test for the independence hypothesis $H_{0}:\mathbf{R}=\mathbf{I}_{m}$, where $\mathbf{I}_{m}$ is the identity matrix of dimension $m$, was first considered by Schott (Biometrika 92 (2005) 951–956) in the high dimensional setting. In this paper, we study the exact power function of this test, under an asymptotic regime in which both $m$ and the sample size $n$ tend to infinity with the ratio $m/n$ upper bounded by a constant. In particular, our result implies that the Rao’s score test is minimax rate-optimal for detecting the dependency signal $\Vert\mathbf{R}-\mathbf{I}_{m}\Vert_{F}$ of order $\sqrt{m/n}$, where $\Vert\cdot\Vert_{F}$ is the matrix Frobenius norm.

Citation

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Dennis Leung. Qiman Shao. "Asymptotic power of Rao’s score test for independence in high dimensions." Bernoulli 25 (1) 241 - 263, February 2019. https://doi.org/10.3150/17-BEJ985

Information

Received: 1 January 2017; Revised: 1 August 2017; Published: February 2019
First available in Project Euclid: 12 December 2018

zbMATH: 07007207
MathSciNet: MR3892319
Digital Object Identifier: 10.3150/17-BEJ985

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 1 • February 2019
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