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Likelihood adaptively modified penalties
Author(s) -
Feng Yang,
Li Tengfei,
Ying Zhiliang
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2322
Subject(s) - consistency (knowledge bases) , stability (learning theory) , estimator , mathematics , coordinate descent , asymptotic distribution , penalty method , strong consistency , model selection , mathematical optimization , regression , selection (genetic algorithm) , computer science , statistics , artificial intelligence , machine learning , geometry
A new family of penalty functions, ie, 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 the stability properties of the penalized maximum‐likelihood estimator, 2 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 approach has competitive performance in comparison with the existing methods.