Projection-Based Inference for High-Dimensional Linear Models

• Activity Number: 310 - Topics of Variable Selection
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Sangyoon Yi* and Xianyang Zhang
• Companies: Texas A&M Univ and Texas A&M University
• Keywords: Con?dence interval; High-dimensional linear models; Lasso; Quadratic programming

Abstract

We develop a new method to estimate the projection direction in the debiased Lasso estimator. The basic idea is to decompose the bias into two terms corresponding to strong and weak signals respectively. We propose to estimate the projection direction by balancing the squared biases associated with the strong and weak signals, and the variance of the debiased Lasso estimator. Standard quadratic programming solver can e?ciently solve the resulting optimization problem. In theory, we show that our projection-based estimator enjoys the asymptotic normality under suitable assumptions. We show that the initial sample size condition can be improved when the magnitudes of weak signals are su?ciently small. The e?ect of the bias and the estimation of the noise level on the coverage accuracy are also studied. We further generalize our method to conduct inference for a linear combination of the regression coe?cients. Simulation studies demonstrate the advantage of the proposed approach concerning coverage accuracy over the original debiased Lasso based on either the normal approximation or the residual bootstrap approximation.