Scrutiny of Inference on Generalized Linear Models with High-Dimensional Covariates

• 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): Lu Xia* and Bin Nan and Yi Li
• Companies: University of Michigan and University of California, Irvine and University of Michigan
• Keywords: Statistical inference; High dimensionality; Generalized linear models; De-sparsifying lasso

Abstract

Statistical inference for high-dimensional models has been gaining its popularity in both statistical theory and real applications. In the existing literature, "de-biasing" or "de-sparsifying" the L1-norm penalized estimator is one of the main stream methods of drawing inference for high-dimensional linear models, and van de Geer et al. (2014) also extended the de-sparsifying approach to generalized linear models (GLMs). We first briefly review the approach of de-sparsifying L1-norm penalized estimator in GLMs (van de Geer et al. 2014) and discuss its potentially practical difficulties, in particular insufficient bias correction and variance estimation. Through extensive simulations in Poisson and logistic regression models, we find that the de-sparsifying approach in GLMs does not work as well as in linear models. Additional discussions are provided, and finally we advocate exercising more cautions of its use.