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The Copula Information Criteria

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  • Steffen Grønneberg
  • Nils Lid Hjort

Abstract

type="main" xml:id="sjos12042-abs-0001"> We derive two types of Akaike information criterion (AIC)-like model-selection formulae for the semiparametric pseudo-maximum likelihood procedure. We first adapt the arguments leading to the original AIC formula, related to empirical estimation of a certain Kullback–Leibler information distance. This gives a significantly different formula compared with the AIC, which we name the copula information criterion. However, we show that such a model-selection procedure cannot exist for copula models with densities that grow very fast near the edge of the unit cube. This problem affects most popular copula models. We then derive what we call the cross-validation copula information criterion, which exists under weak conditions and is a first-order approximation to exact cross validation. This formula is very similar to the standard AIC formula but has slightly different motivation. A brief illustration with real data is given.

Suggested Citation

  • Steffen Grønneberg & Nils Lid Hjort, 2014. "The Copula Information Criteria," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 436-459, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:436-459
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    File URL: http://hdl.handle.net/10.1111/sjos.12042
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    References listed on IDEAS

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    1. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    2. Panchenko, Valentyn, 2005. "Goodness-of-fit test for copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 176-182.
    3. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    4. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    5. Ko, Vinnie & Hjort, Nils Lid, 2019. "Copula information criterion for model selection with two-stage maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 12(C), pages 167-180.
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    14. Elisa Perrone & Andreas Rappold & Werner G. Müller, 2017. "$$D_s$$ D s -optimality in copula models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 403-418, August.
    15. Einolander, Johannes & Lahdelma, Risto, 2022. "Multivariate copula procedure for electric vehicle charging event simulation," Energy, Elsevier, vol. 238(PA).
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