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An information criterion for model selection with missing data via complete-data divergence

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  • Hidetoshi Shimodaira

    (Osaka University
    RIKEN Center for Advanced Intelligence Project)

  • Haruyoshi Maeda

    (Osaka University
    Kawasaki Heavy Industries, Ltd.)

Abstract

We derive an information criterion to select a parametric model of complete-data distribution when only incomplete or partially observed data are available. Compared with AIC, our new criterion has an additional penalty term for missing data, which is expressed by the Fisher information matrices of complete data and incomplete data. We prove that our criterion is an asymptotically unbiased estimator of complete-data divergence, namely the expected Kullback–Leibler divergence between the true distribution and the estimated distribution for complete data, whereas AIC is that for the incomplete data. The additional penalty term of our criterion for missing data turns out to be only half the value of that in previously proposed information criteria PDIO and AICcd. The difference in the penalty term is attributed to the fact that our criterion is derived under a weaker assumption. A simulation study with the weaker assumption shows that our criterion is unbiased while the other two criteria are biased. In addition, we review the geometrical view of alternating minimizations of the EM algorithm. This geometrical view plays an important role in deriving our new criterion.

Suggested Citation

  • Hidetoshi Shimodaira & Haruyoshi Maeda, 2018. "An information criterion for model selection with missing data via complete-data divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 421-438, April.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:2:d:10.1007_s10463-016-0592-7
    DOI: 10.1007/s10463-016-0592-7
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    References listed on IDEAS

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    3. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    4. Gerda Claeskens & Fabrizio Consentino, 2008. "Variable Selection with Incomplete Covariate Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1062-1069, December.
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