Sure Screening and Refitted Crossvalidation for Ultra High-Dimensional Statistical Inferences

• Activity Number: 440
• Type: Invited
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Jianqing Fan*+ and Shaojun Guo and Ning Hao
• Companies: Princeton University and Chinese Academy of Sciences and Princeton University
• Keywords: Refitted Cross-validation ; Variance Estimation ; Ultrahigh dimensionality ; Sure screening

Abstract

In ultrahigh dimensional linear regressions, traditional variance estimation techniques are not applicable. One of the major problems in ultrahigh dimensional regression is the high spurious correlation between the unobserved realized noise and some of the predictors. As a result, the realized noises are actually predicted when extra irrelevant variables are selected, leading to serious underestimate of the noise level. We propose a two-stage refitted procedure via a data splitting technique, called refitted cross-validation (RCV), to attenuate the influence of irrelevant variables with high spurious correlations. Our asymptotic results show that the resulting procedure performs as well as the oracle estimator. The simulation studies lend further support to our theoretical claims. The naive two-stage estimator and the plug-in one stage estimators are also studied and compared.