Bias reduction and model selection in misspecified models

Abstract

This article concerns maximum penalized likelihood estimation in misspecified generalized linear models with independent and identically distributed observations. A new method for simultaneous model selection and estimation with bias reduction is proposed in the framework. A discontinuous penalized likelihood function is used, and an approximate method to solve the discontinuous optimization problem is introduced. The proposed method has model selection consistency in a sparse regression setting in which the dimension of predictors is fixed and the sample size increases. The efficiency of the proposed method is illustrated through a finite simulation study.

Keywords:

• Bias reduction
• model selection
• penalized likelihood

Acknowledgments

The author would like to thank the Editor and two anonymous referees for comments that have improved the manuscript considerably.