Asymptotic bootstrap corrections of AIC for linear regression models

Abd Krim Seghouane*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    48 Citations (Scopus)

    Abstract

    The Akaike information criterion, AIC, and its corrected version, AICc are two methods for selecting normal linear regression models. Both criteria were designed as estimators of the expected Kullback-Leibler information between the model generating the data and the approximating candidate model. In this paper, two new corrected variants of AIC are derived for the purpose of small sample linear regression model selection. The proposed variants of AIC are based on asymptotic approximation of bootstrap type estimates of Kullback-Leibler information. These new variants are of particular interest when the use of bootstrap is not really justified in terms of the required calculations. As its the case for AICc, these new variants are asymptotically equivalent to AIC. Simulation results which illustrate better performance of the proposed AIC corrections when applied to polynomial regression in comparison to AIC, AICc and other criteria are presented. Asymptotic justifications for the proposed criteria are provided in the Appendix.

    Original languageEnglish
    Pages (from-to)217-224
    Number of pages8
    JournalSignal Processing
    Volume90
    Issue number1
    DOIs
    Publication statusPublished - Jan 2010

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