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Activity Number: 163 - Biometrics Section Byar Award Student Paper Session II
Type: Topic Contributed
Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 11:50 AM
Sponsor: Biometrics Section
Abstract #312252
Title: A Revisit to De-Biased Lasso for Generalized Linear Models
Author(s): Lu Xia* and Bin Nan and Yi Li
Companies: University of Michigan, Ann Arbor and University of California, Irvine and University of Michigan
Keywords: Confidence interval; Coverage; High-dimension; Inverse of information matrix; Statistical inference

De-biased lasso has emerged as a popular tool to draw statistical inference for high-dimensional regression models. However, simulations indicate that for generalized linear models (GLMs), de-biased lasso inadequately removes biases and yields unreliable confidence intervals. This motivates us to scrutinize the application of de-biased lasso in high-dimensional GLMs. When p>n, we detect that a key sparsity condition on the inverse information matrix generally does not hold in a GLM setting, which likely explains the subpar performance of de-biased lasso. Even in a less challenging “large n, diverging p” scenario, we find that de-biased lasso and the maximum likelihood method often yield confidence intervals with unsatisfactory coverage probabilities. In this scenario, we examine an alternative approach for further bias correction by directly inverting the Hessian matrix without imposing the matrix sparsity assumption. We establish the asymptotic theory for the resulting estimates, which lays the theoretical groundwork for drawing inference, and illustrate the performance with simulation studies and analysis of a prospective hospital-based Boston Lung Cancer Study.

Authors who are presenting talks have a * after their name.

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