CMStatistics 2022: Start Registration
View Submission - CMStatistics
Title: Robust variable selection in semiparametric regression modeling Authors:  Seo-Young Park - Sungkyunkwan University (Korea, South) [presenting]
Byungtae Seo - Sungkyunkwan University (Korea, South)
Abstract: The penalized least squares and maximum likelihood methods have been successfully employed for simultaneous parameter estimation and variable selection. However, outlying observations can severely affect the quality of the estimator and selection performance. Although some robust methods for variable selection have been proposed in the literature, they often lose substantial efficiency. This is because the tool to gain robustness depends excessively on choosing additional tuning parameters or modifying the original objective functions. To alleviate such issues, we propose a penalized maximum likelihood method using a nonparametric Gaussian scale mixture distribution. We demonstrate that the proposed estimator has desirable theoretical properties, including sparsity and oracle properties. For the estimation, we alternatively exploit expectation-maximization and gradient-based algorithms for the parametric and nonparametric components, respectively. We also demonstrate the performance of the proposed method through numerical studies, including simulation studies and real data analysis.