Error Variance Estimation in Ultra-High Dimensional Regression Models

• Activity Number: 101 - Foundation for Big Data Analysis
• Type: Invited
• Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Runze Li* and Zhao Chen and Jianqing Fan
• Companies: The Pennsylvania State University and The Pennsylvania State University and Princeton University
• Keywords: Feature screening ; Refitted cross-validation ; Sparse additive model ; Variance estimation

Abstract

Error variance estimation plays an important role in statistical inference for high dimensional regression models. This presentation concerns with error variance estimation in high dimensional sparse models. This talk will start with the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to spurious correlations. This talk further presents an accurate estimate for error variance in ultrahigh dimensional sparse model by effectively integrating sure independence screening and refitted cross-validation techniques. The root n consistency and the asymptotic normality of the resulting estimate are established. Monte Carlo simulation study are conducted to examine the finite sample performance of the newly proposed estimate. A real data example is used to illustrate the proposed methodology.