Main Article Content
This paper proposes a method for constructing a predictive estimator for logistic regression. We make a provisional assumption that the predictive estimator is given by multiplying the maximum likelihood estimators by constants, which are estimated using a parametric bootstrap method. The relative merits of the maximum likelihood estimator and the predictive estimator produced by this method are determined by cross-validation. The results show that the predictive
estimators derived by this method lead to a smaller deviance than that obtained by the maximum likelihood estimator in many instances.
Takezawa K. A revision of AIC for normal error models. Open Journal of Statistics. 2012;2(3):309-312.
Takezawa K. Learning regression analysis by simulation. Springer, Tokyo, Japan; 2014.
Takezawa K. Estimation of the exponential distribution in the light of future data. British Journal of Mathematics & Computer Science. 2015;5(1):128-132.
Ogasawara H. Predictive estimation of a covariance matrix and its structural parameters. Journal of the Japanese Society of Computational Statistics. 2017;30:45-63.
Ogasawara H. A family of the adjusted estimators maximizing the asymptotic predictive expected log-likelihood. Behaviormetrika. 2017;44:57-95.
Ogasawara H. An asymptotic equivalence of the cross-data and predictive estimators. Communications in Statistics - Theory and Methods. 2019;1-14.
Mc Cullagh P, Nelder JA. Generalized linear models, second edition. Chapman & Hall/CRC. Boca Raton, FL, U.S.A.; 1989.
Myers RH, Montgomery DC. Vining GG, Robinson TJ. Generalized Linear Models: With Applications in Engineering and the Sciences (first edition). Wiley. NJ, U.S.A.; 2002.
Wood SN. Generalized additive models: An introduction with R, second edition. Chapman & Hall/CRC. Boca Raton, FL, U.S.A.; 2017.
Dobson AJ, Barnett AG. An introduction to generalized linear models, fourth edition. Chapman & Hall/CRC. Boca Raton, FL, U.S.A.; 2018.
Takezawa K. Predictive estimator for simple regression. Journal of Advances in Mathematics and Computer Science. 2017;24(4):1-14.
Efron B, Tibshirani RJ. An introduction to the bootstrap. Chapman & Hall/CRC. Boca Raton, FL, U.S.A.; 1993.
Takezawa K. Optimal estimator with respect to expected log-likelihood. International Journal of Innovation in Science and Mathematics. 2014;2(6):494-508.
James G, Witten G, Hastie D, Tibshirani T, James R. An introduction to statistical learning: With applications in R. New York: Springer; 2013.
Akaike H. Information theory and an extension of the maximum likelihood principle. Proceedings of 2nd International Symposium on Information Theory (Petrov BN. Csaki F. (Eds.)),. Budapest: Akademiai Kiado. 1973;267-281.
Akaike H. A new look at the statistical model identification. IEEE Transaction on Automatic Control. 1974;19(6):716-723.
Konishi S, Kitagawa G. Information criteria and statistical modelling. New York: Springer; 2008.
Wahba G. Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics). Society for Industrial and Applied Mathematics; 1990.
Golub GH, Heath M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics. 1979;21(2):215-223.
Efron B. Estimating the error rate of a prediction rule: improvement on cross-validation. Journal of the American Statistical Association. 1983;78;316-331.
Efron B, Tibshirani RJ. Improvements on cross-validation: The .632+ bootstrap method. Journal of the American Statistical Association. 1997;92(438):548-560.
Arlot S, Celisse A. A survey of cross-validation procedures for model selection. Statistics Surveys. 2010;4;40-79.
Friedman JH, Hastie T, Tibshirani R. Regularized paths for generalized linear models via coordinate descent. Journal of Statistical Software. 2010;33(1);1-22.
Hastie T, Qian J. Glmnet Vignette. Stanford; 2016.
Available:https://web.stanford.edu/ hastie/Papers/GlmnetV ignette:pdf