An asymptotic equivalence of the cross-data and predictive estimators

Haruhiko Ogasawara

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 3, 755-768

Abstract: Estimators using multiplicative tuning parameters for maximum likelihood estimators in cross-validation are called cross-data estimators in this paper. Single-sample versions of the cross-data estimators have been called predictive estimators in literatures, which are given by maximizing the expected log-likelihood, where the two-fold expectations are taken over the distributions of future and current data using maximum likelihood estimators based on current data. An asymptotic equivalence of the cross-data and predictive estimators is shown, which guarantees an optimality of the predictive estimator when an unknown population parameter vector is replaced by the sample counterpart. Examples using typical statistical distributions are shown.

Date: 2020
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DOI: 10.1080/03610926.2018.1549258

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