论文摘要：Variance estimation is a fundamental problem in statistical modeling. In ultrahigh dimensional linear regression where the dimensionality is much larger than sample size, traditional variance estimation techniques are not applicable. Recent advances on variable selection in ultrahigh dimensional linear regression make this problem accessible. One of the major problems in ultrahigh dimensional regression is the high spurious corre-lation 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. In this paper, 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, which knows in advance themean regression function. The simulation studies lend further support to our theoretical claims. The naive two-stage estimator and the plug-in one stage estimators using LASSO and SCAD are also studied and compared.Their performances can be improved by the proposed RCV method。

论文题目: Variance Estimation Using Refitted Cross-validation in Ultrahigh Dimensional Regression

论文作者: Jianqing FAN, Shaojun GUO (郭绍俊) and Ning HAO

发表刊物: Journal of the Royal Statisitical Society, Series B（已接受）