Likelihood Adaptively Modified Penalties
This work provides an incremental improvement in model selection techniques for regression analysis, potentially benefiting statisticians and data scientists.
The authors introduced a new family of likelihood-adaptive penalty functions for model selection in regression models, which arises from specific prior distributions on parameters. They established theoretical properties including consistency and asymptotic stability, and demonstrated through simulations and real data that the method achieves competitive performance compared to existing approaches.
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.