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

作　　者：GUO WenWen CHEN YongShuai CUI HengJian 

机构地区：[1]School of Mathematical Sciences, Capital Normal University

出　　处：《Science China Mathematics》2016年第12期2319-2334,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11071022, 11231010 and 11471223);Beijing Center for Mathematics and Information Interdisciplinary Science;Key Project of Beijing Municipal Educational Commission (Grant No. KZ201410028030)

摘　　要：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.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.

关 键 词：high dimension regression large p small n refitted cross-validation variance estimation U-type test robust 

分 类 号：O212.1[理学—概率论与数理统计]