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On Parametric Bootstrapping and Bayesian Prediction

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  • Tadayoshi Fushiki
  • Fumiyasu Komaki
  • Kazuyuki Aihara

Abstract

. We investigate bootstrapping and Bayesian methods for prediction. The observations and the variable being predicted are distributed according to different distributions. Many important problems can be formulated in this setting. This type of prediction problem appears when we deal with a Poisson process. Regression problems can also be formulated in this setting. First, we show that bootstrap predictive distributions are equivalent to Bayesian predictive distributions in the second‐order expansion when some conditions are satisfied. Next, the performance of predictive distributions is compared with that of a plug‐in distribution with an estimator. The accuracy of prediction is evaluated by using the Kullback–Leibler divergence. Finally, we give some examples.

Suggested Citation

  • Tadayoshi Fushiki & Fumiyasu Komaki & Kazuyuki Aihara, 2004. "On Parametric Bootstrapping and Bayesian Prediction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 403-416, September.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:3:p:403-416
    DOI: 10.1111/j.1467-9469.2004.02_127.x
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    Cited by:

    1. Zhang, Fode & Shi, Yimin, 2016. "Geometry of exponential family with competing risks and censored data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 234-245.
    2. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.

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