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2013 Rank-based score tests for high-dimensional regression coefficients
Long Feng, Changliang Zou, Zhaojun Wang, Bin Chen
Electron. J. Statist. 7: 2131-2149 (2013). DOI: 10.1214/13-EJS839

Abstract

This article is concerned with simultaneous tests on linear regression coefficients in high-dimensional settings. When the dimensionality is larger than the sample size, the classic $F$-test is not applicable since the sample covariance matrix is not invertible. Recently, [5] and [17] proposed testing procedures by excluding the inverse term in $F$-statistics. However, the efficiency of such $F$-statistic-based methods is adversely affected by outlying observations and heavy tailed distributions. To overcome this issue, we propose a robust score test based on rank regression. The asymptotic distributions of the proposed test statistic under the high-dimensional null and alternative hypotheses are established. Its asymptotic relative efficiency with respect to [17]’s test is closely related to that of the Wilcoxon test in comparison with the $t$-test. Simulation studies are conducted to compare the proposed procedure with other existing testing procedures and show that our procedure is generally more robust in both sizes and powers.

Citation

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Long Feng. Changliang Zou. Zhaojun Wang. Bin Chen. "Rank-based score tests for high-dimensional regression coefficients." Electron. J. Statist. 7 2131 - 2149, 2013. https://doi.org/10.1214/13-EJS839

Information

Published: 2013
First available in Project Euclid: 23 August 2013

zbMATH: 1349.62218
MathSciNet: MR3104951
Digital Object Identifier: 10.1214/13-EJS839

Subjects:
Primary: 62H15
Secondary: 62G20, 62J05

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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