Minimax concave bridge penalty function for variable selection

Abstract

This thesis focuses on one of the most important aspect of statistics - variable selection. Penalized regression, with its wide spectrum of penalty functions to meet different underlying data structures, is a popular variable selection procedure. In this thesis, we provide a penalty function called the Minimax Concave Bridge Penalty (MCBP) for the implementation of penalized regression that will perform variable selection and address the issue of separation in logistic regression. The MCBP function is a product that draws strengths from existing penalty functions and is flexibly adapted to achieve the characteristics required of penalty function to possess the different desired properties of variable selection. The MCBP function is inevitably nonconvex and this translates to numerical challenges in optimization with MCBP function. In this thesis, we also provide a matching computation algorithm, via concave-convex procedure, to facilitate the fitting of MCBP models.