Robust U-type test for high dimensional regression coefficients using refitted cross-validation variance estimation

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• 作者：WenWen Guo ; YongShuai Chen ; HengJian Cui
• 关键词：high dimension regression ; large p ; small n ; refitted cross ; validation variance estimation ; U ; type test ; robust
• 刊名：Science China Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：59
• 期：12
• 页码：2319-2334
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：59

文摘

This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that the limiting null distribution of the proposed new test is normal under two kinds of ordinary models. We further study the local power of the proposed test and compare with other competitive tests for high dimensional data. The idea of refitted cross-validation approach is utilized to reduce the bias of sample variance in the estimation of the test statistic. Our theoretical results indicate that the proposed test can have even more substantial power gain than the test by Zhong and Chen (2011) when testing a hypothesis with outlying observations and heavy tailed distributions. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo studies. We also illustrate the application of the proposed test by an empirical analysis of a real data example.