Semiparametric model selection with applications to regression

We consider model selection problem using samples of small or moderate size where each model can have unknown parameter without a fully specified likelihood function. A semiparametric model selection criterion is proposed where the penalty-based model complexity term is used for the parameter with fully specified model structure and the kernel density estimation is used for the unknown noise distribution. A linear regression problem with various noise distributions is studied and the numerical results reveal that the semiparametric approach outperforms the penalty-based criteria and cross validation.