Semi-Parametric Model Selection Using AIC and BIC under the Curse of Dimensionality: A Monte Carlo Investigation

Abstract

This article investigates the performance of two common information criteria, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) in choosing among three semiparametric regression models, i.e., the single-index model (SIM), the partial linear model (PLM), and the additive model (AM). The paper also includes a Monte Carlo experiment for various sample sizes and dimensions (n = 50, 100, 200) and (p = 10, 30). According to AIC and BIC, the best model for each simulated data set is the model with the minimum value of the information criterion. CMSR considers the model selection-based efficiency of AIC and BIC, while APE measures predictive performance. AIC and BIC are functions of the sample size and the dimensionality but versus the simulation results of the competing semiparametric models, they seem to behave antithetically for certain competing semi parametric models on the page. However the precision of both criteria can be further increased in model selection and prediction by a larger sample size. Results further indicate that for the increasing sample size, the PLM produces the least prediction error when compared with the SIM and the AM