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Estimating the Kullback–Liebler risk based on multifold cross-validation

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  • Paolo Vidoni

Abstract

type="main" xml:id="stan12070-abs-0001"> This paper concerns a class of model selection criteria based on cross-validation techniques and estimative predictive densities. Both the simple or leave-one-out and the multifold or leave-m-out cross-validation procedures are considered. These cross-validation criteria define suitable estimators for the expected Kullback–Liebler risk, which measures the expected discrepancy between the fitted candidate model and the true one. In particular, we shall investigate the potential bias of these estimators, under alternative asymptotic regimes for m. The results are obtained within the general context of independent, but not necessarily identically distributed, observations and by assuming that the candidate model may not contain the true distribution. An application to the class of normal regression models is also presented, and simulation results are obtained in order to gain some further understanding on the behavior of the estimators.

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  • Paolo Vidoni, 2015. "Estimating the Kullback–Liebler risk based on multifold cross-validation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 510-540, November.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:4:p:510-540
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    References listed on IDEAS

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    1. Yasunori Fujikoshi & Takafumi Noguchi & Megu Ohtaki & Hirokazu Yanagihara, 2003. "Corrected versions of cross-validation criteria for selecting multivariate regression and growth curve models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 537-553, September.
    2. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    3. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    4. Yanagihara, Hirokazu & Tonda, Tetsuji & Matsumoto, Chieko, 2006. "Bias correction of cross-validation criterion based on Kullback-Leibler information under a general condition," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1965-1975, October.
    5. Hirokazu Yanagihara & Hironori Fujisawa, 2012. "Iterative Bias Correction of the Cross‐Validation Criterion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 116-130, March.
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