Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 3, 566--581

Repeated Half Sampling Criterion for Model Selection


B. Hafidi and A. Mkhadri, Cadi-Ayyad University, Marrakech, Morocco

SUMMARY. In this paper, the asymptotic property and the performance of the repeated half sampling (RHS) criterion are investigated. In the context of variable selection under a linear regression model, we show that RHS is asymptotically equivalent to the multifold cross-validated (MCV) criterion. While in the case where the candidate family of models doesn't include the true model, we establish that RHS and also MCV are asymptotically equivalent to a criterion similar to Takeuchi information criterion (TIC). The performance of RHS criterion is compared with CV, Akaike, corrected Akaike and BIC criteria. The results of a simulation study show that RHS improve upon the performance of some criteria in two important areas of application: multiple linear regression and multivariate regression.

AMS (1991) subject classification}. Primary 62J05; secondary 62E20.

Key words and phrases. Model selection, repeated half sampling, regression, cross-validation, TIC criterion.

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