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Original Articles

Asymptotic biases of information and cross-validation criteria under canonical parametrization

Pages 964-985 | Received 13 Jul 2017, Accepted 22 Dec 2017, Published online: 09 Mar 2018

References

  • Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. In Proceedings of the 2nd international symposium on information theory, ed. B. N. Petrov, and F. Csáki, 267–281. Budapest: Académiai Kiado.
  • Allen, D. M. 1971a. Mean square error of prediction as a criterion for selecting variables. Technometrics, 13:469–475. doi:10.1080/00401706.1971.10488811.
  • Allen, D. M. 1971b. The prediction sum of squares as a criterion for selecting predictor variables. Technical Report, Number 23, Department of Statistics, University of Kentucky.
  • Browne, M. W. 2000. Cross-validation methods. Journal of Mathematical Psychology, 44:108–132. doi:10.1006/jmps.1999.1279.
  • Davies, S. L., A. A. Neath, and J. E. Cavanaugh 2005. Cross validation model selection criteria for linear regression based on the Kullback-Leibler discrepancy. Statistical Methodology, 2:249–266. doi:10.1016/j.stamet.2005.05.002.
  • Fujikoshi, Y., T. Noguchi, M. Ohtaki, & H. Yanagihara 2003. Corrected versions of cross-validation criteria for selecting multivariate regression and growth curve models. Annals of the Institute of Statistical Mathematics, 55:537–553. doi:10.1007/BF02517806.
  • Fujikoshi, Y., and K. Satoh 1997. Modified AIC and Cp in multivariate linear regression. Biometrika, 84:707–716. doi:10.1093/biomet/84.3.707.
  • Fujikoshi, Y., H. Yanagihara, and H. Wakaki 2005. Bias corrections of some criteria for selecting multivariate linear models in a general nonnormal case. American Journal of Mathematical and Management Sciences, 25:221–258. doi:10.1080/01966324.2005.10737651.
  • Hurvich, C. M., and C.-L. Tsai 1989. Regression and time series model selection in small samples. Biometrika, 76:297–307. doi:10.1093/biomet/76.2.297.
  • Kullback, S., and R. A. Leibler 1951. On information and sufficiency. The Annals of Mathematical Statistics, 22:79–86. doi:10.1214/aoms/1177729694.
  • Mardia, K. V. 1970. Measures of multivariate skewness and kurtosis with applications. Biometrika, 57:519–530. doi:10.1093/biomet/57.3.519.
  • Mòri, T. F., V. K. Rohatgi, and G. J. Székely 1993. On multivariate skewness and kurtosis. Theory of Probability and Its Applications, 38:547–551. doi:10.1137/1138055.
  • Ogasawara, H. 2016a. Asymptotic cumulants of some information criteria. Journal of the Japanese Society of Computational Statistics, 29:1–25. doi:10.5183/jjscs.1512001_225.
  • Ogasawara, H. 2016b. Supplement I to the paper “Asymptotic cumulants of some information criteria” – Proofs and technical results. Economic Review (Otaru University of Commerce), 67 (2 & 3):9–44. Permalink: http://hdl.handle.net/10252/00005592, http://www.res.otaru-uc.ac.jp/∼emt-hogasa/.
  • Ogasawara, H. 2017a. Supplement III to the paper “Asymptotic cumulants of some information criteria” – Examples 2 and 3. Economic Review (Otaru University of Commerce), 68 (1):1–65. Permalink: http://hdl.handle.net/10252/00005680, http://www.res.otaru-uc.ac.jp/∼emt-hogasa/.
  • Ogasawara, H. 2017b. Extensions of Pearson's inequality between skewness and kurtosis to multivariate cases. Statistics and Probability Letters, 130:12–16. doi:10.1016/j.spl.2017.07.003.
  • Pearson, K. 1916. IX. Mathematical contributions to the theory of evolution. – XIX. Second supplement to a memoir on skew variation. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 216:429–457.
  • Shibata, R. 1997. Bootstrap estimate of Kullback-Leibler information for model selection. Statistica Sinica, 7:375–394.
  • Stone, M. 1974. Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, B, 36:111–147.
  • Stone, M. 1977. An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. Journal of the Royal Statistical Society, B, 39:44–47.
  • Takeuchi, K. 1976. Distributions of information statistics and criteria of the goodness of models. Mathematical Science, 153:12–18. (in Japanese)
  • Yanagihara, H. 2006. Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case. Journal of Multivariate Analysis, 97:1070–1089. doi:10.1016/j.jmva.2005.06.005.
  • Yanagihara, H., and H. Fujisawa 2012. Iterative bias correction of the cross-validation criterion. Scandinavian Journal of Statistics, 39:116–130. doi:10.1111/j.1467-9469.2011.00754.x.
  • Yanagihara, H., T. Tonda, and C. Matsumoto 2006. Bias correction of cross-validation criterion based on Kullback-Leibler information under a general condition. Journal of Multivariate Analysis, 97:1965–1975. doi:10.1016/j.jmva.2005.10.009.
  • Yanagihara, H., K.-H. Yuan, H. Fujisawa, and K. Hayashi 2013. A class of model selection criteria based on cross-validation method. Hiroshima Mathematical Journal, 43:149–177.

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