Abstract
In this paper, we introduce a new class of robust model selection criteria. These criteria are defined by estimators of the expected overall discrepancy using pseudodistances and the minimum pseudodistance principle. Theoretical properties of these criteria are proved, namely asymptotic unbiasedness, robustness, consistency, as well as the limit laws. The case of the linear regression models is studied and a specific pseudodistance based criterion is proposed. Monte Carlo simulations and applications for real data are presented in order to exemplify the performance of the new methodology. These examples show that the new selection criterion for regression models is a good competitor of some well known criteria and may have superior performance, especially in the case of small and contaminated samples.
Highlights
Model selection is fundamental to the practical applications of statistics and there is a substantial literature on this issue
In order to illustrate the performance of the Pseudodistance based Information Criterion (PIC) criterion (44) in the case of linear regression models, we performed a simulation study using for comparison the model selection criteria Akaike Information Criterion (AIC), BayesianInformation Criterion (BIC)
We proved theoretical properties of these criteria including asymptotic unbiasedness, robustness, consistency, as well as the limit laws
Summary
Model selection is fundamental to the practical applications of statistics and there is a substantial literature on this issue. The minimum pseudodistance estimators for general parametric models have been studied in [15] and consist of minimizing an empirical version of a pseudodistance between the assumed theoretical model and the true model underlying the data These estimators have the advantage of not requiring any prior smoothing and conciliate robustness with high efficiency, providing a high degree of stability under model misspecification, often with a minimal loss in model efficiency. In the present paper we propose new criteria for model selection, based on pseudodistances and on minimum pseudodistance estimators. These new criteria have robustness properties, are asymptotically unbiased, consistent and compare well with some other known model selection criteria, even for small samples.
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