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A family of the information criteria using the phi-divergence for categorical data

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  • Ogasawara, Haruhiko

Abstract

The risk of the phi-divergence of a statistical model for categorical data is defined using two independent sets of data. The asymptotic bias of the phi-divergence based on current data as an estimator of the risk is shown to be equal to the negative penalty term of the Akaike information criterion (AIC). Though the higher-order asymptotic bias is derived, the higher-order bias depends on the form of the phi-divergence and the estimation method of parameters using a possible different form of the phi-divergence. An approximation to the higher-order bias is obtained based on the simple result of the saturated model. The information criteria using this approximation yield improved results in simulations for model selection. Some cases of the phi-divergences show advantages over the AIC in simulations.

Suggested Citation

  • Ogasawara, Haruhiko, 2018. "A family of the information criteria using the phi-divergence for categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 87-103.
    • Handle: RePEc:eee:csdana:v:124:y:2018:i:c:p:87-103
    DOI: 10.1016/j.csda.2018.03.001
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    References listed on IDEAS

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    1. N. Martín & L. Pardo, 2008. "Minimum phi-divergence estimators for loglinear models with linear constraints and multinomial sampling," Statistical Papers, Springer, vol. 49(1), pages 15-36, March.
    2. Ogasawara, Haruhiko, 2017. "Expected predictive least squares for model selection in covariance structures," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 151-164.
    3. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 317-332, September.
    4. Ogasawara, Haruhiko, 2016. "Bias correction of the Akaike information criterion in factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 144-159.
    5. Haruhiko Ogasawara, 2009. "Asymptotic cumulants of the parameter estimators in item response theory," Computational Statistics, Springer, vol. 24(2), pages 313-331, May.
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