A new nonparametric test for high-dimensional regression coefficients

ABSTRACT

Several tests for high-dimensional (large p, small n) regression coefficients have been proposed in the recent literature, but they are adversely affected by outlying observations and heavy-tailed distributions. In order to attack these challenges, a novel nonparametric testing procedure is developed under the framework of rank-based inference and is robust with respect to both the responses and the covariates. Besides, the proposed test statistic is invariant under the group of scalar transformations, which implies that our test statistic can integrate all the individual information in a relatively fair way. The newly defined test has many desirable general asymptotic properties, such as normality and consistency when $(n,p)\to \mathrm{\infty }.$ We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo simulation, which demonstrates an improvement over the previous literature.

KEYWORDS:

• Large p
• small n
• high-dimensional regression
• rank regression
• Wilcoxon's test

AMS SUBJECT CLASSIFICATION:

• 62H15
• 62G20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11371236 and grant number 11201005] and the Graduate Student Innovation Foundation of Shanghai University of Finance and Economics [CXJJ-2015-440].