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An asymptotic equivalence of the cross-data and predictive estimators

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  • Haruhiko Ogasawara

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.

Suggested Citation

  • Haruhiko Ogasawara, 2020. "An asymptotic equivalence of the cross-data and predictive estimators," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(3), pages 755-768, February.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:3:p:755-768
    DOI: 10.1080/03610926.2018.1549258
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