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Dominance of posterior predictive densities over plug-in densities for order statistics in exponential distributions

Author

Listed:
  • Kouhei Nishi

    (Tokyo University of Science)

  • Takeshi Kurosawa

    (Tokyo University of Science)

  • Nobuyuki Ozeki

    (Tokyo University of Science)

Abstract

Many researchers have proposed numerous Bayesian predictive densities for Type-II censored data that is generated by ordered observations. However, their evaluations of predictive densities were insufficient because the Bayesian predictive density includes prior parameters, thus we suffer from the selection of the prior parameters. In this study, we consider two types of predictive densities, posterior predictive and plug-in, for observations from an exponential distribution of Type-II censored data. We discuss a suitable predictive density using the risk with the Kullback–Leibler loss function. In our setting, we consider a Gamma prior, which is a conjugate prior for mathematical tractability. We prove that the posterior predictive density with an improper Gamma prior provides the dominance of the posterior predictive density over the plug-in densities without depending on the selection of an unknown parameter in our setting. Finally, we show that the posterior predictive density outperforms the plug-in densities in terms of coverage probabilities for unobserved data by censoring in a simulation study.

Suggested Citation

  • Kouhei Nishi & Takeshi Kurosawa & Nobuyuki Ozeki, 2024. "Dominance of posterior predictive densities over plug-in densities for order statistics in exponential distributions," Computational Statistics, Springer, vol. 39(4), pages 2291-2321, June.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01423-8
    DOI: 10.1007/s00180-023-01423-8
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    References listed on IDEAS

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    1. Kengo Kato, 2009. "Improved prediction for a multivariate normal distribution with unknown mean and variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 531-542, September.
    2. repec:dau:papers:123456789/1908 is not listed on IDEAS
    3. A. Boisbunon & Y. Maruyama, 2014. "Inadmissibility of the best equivariant predictive density in the unknown variance case," Biometrika, Biometrika Trust, vol. 101(3), pages 733-740.
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