Electronic Journal of Statistics

Rank-based score tests for high-dimensional regression coefficients

Long Feng, Changliang Zou, Zhaojun Wang, and Bin Chen

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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.

Article information

Electron. J. Statist., Volume 7 (2013), 2131-2149.

First available in Project Euclid: 23 August 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H15: Hypothesis testing
Secondary: 62G20, 62J05

Asymptotic normality high-dimensional data large $p$, small $n$ rank regression wicoxon test


Feng, Long; Zou, Changliang; Wang, Zhaojun; Chen, Bin. Rank-based score tests for high-dimensional regression coefficients. Electron. J. Statist. 7 (2013), 2131--2149. doi:10.1214/13-EJS839. https://projecteuclid.org/euclid.ejs/1377268991

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