Likelihood Adaptively Modified Penalties

TL;DR

This paper introduces a new likelihood-adaptive penalty function for model selection in regression, demonstrating theoretical consistency, stability, and competitive performance through simulations and real data analysis.

Contribution

It proposes a novel adaptive penalty based on likelihood, with proven theoretical properties and an efficient algorithm, advancing model selection methods in regression analysis.

Findings

The method achieves parameter estimation consistency.

It ensures model selection consistency.

It performs competitively in simulations and real data.

Abstract

A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study stability properties of the penalized maximum likelihood estimator, two types of asymptotic stability are defined. Theoretical properties, including the parameter estimation consistency, model selection consistency, and asymptotic stability, are established under suitable regularity conditions. An efficient coordinate-descent algorithm is proposed. Simulation results and real data analysis show that the proposed method has competitive performance in comparison with existing ones.