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A Predictive Density Criterion for Selecting Non-Nested Linear Models and Comparison with Other Criteria

In: Probability and Bayesian Statistics

Author

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  • Hajime Wago

    (Tsukuba University)

  • Hiroki Tsurumi

    (Rutgers University)

Abstract

The mean squared-errors of forecasts (MSEF) is a statistic used to evaluate post-sample prediction performance. The MSEF has been used as a descriptive measure, but its exact distribution can be derived either from a sample theoretical or from a Bayesian perspective if the MSEF is computed from a linear regression model. In this paper, Bayesian and sampling distributions of the MSEF are derived, and it is suggested that the MSEF may be used as a statistic for linear model selection. Using sampling experiments, we compare the MSEF criterion with other model selection criteria. The organization of the paper is as follows. In section 2, we give the Bayesian and sampling distributions of the MSEF. In section 3, after presenting Akaike’s information criterion, AIC, [Akaike (1974)], Efron’s confidence interval for the mean squared errors, the N- and J-tests, we make sampling experiments to compare the Bayesian MSEF criterion with these other criteria.

Suggested Citation

  • Hajime Wago & Hiroki Tsurumi, 1987. "A Predictive Density Criterion for Selecting Non-Nested Linear Models and Comparison with Other Criteria," Springer Books, in: R. Viertl (ed.), Probability and Bayesian Statistics, pages 477-486, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1885-9_49
    DOI: 10.1007/978-1-4613-1885-9_49
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