Title: Post-selection inference on high-dimensional varying-coefficient generalized linear models
Authors: Ran Dai - University of Nebraska Medical Center (United States) [presenting]
Cheng Zheng - University of Wisconsin - Milwaukee (United States)
Abstract: Generalized linear models (GLMs) are important parametric extensions of linear models. Varying-coefficient modeling is frequently used in capturing the dynamics of the impact of the covariates. We study high-dimensional varying-coefficient generalized linear models, which allow us to capture non-stationary effects of the input variables across time. We develop new tools for the statistical inference that allow us to construct valid confidence intervals and honest tests for nonparametric coefficients at fixed varying-coefficient indices. The focus is on inference in a high-dimensional setting where the number of input variables exceeds the sample size. Performing statistical inference in this regime is challenging due to the usage of model selection techniques in estimation. Nevertheless, we develop valid inferential tools that are applicable to a wide range of data generating processes and do not suffer from biases introduced by model selection. We performed numerical simulations to demonstrate the finite sample performance of our method and we also illustrate the application with a real data example.