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Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location

Author

Listed:
  • Yasuyuki Hamura

    (University of Tokyo)

  • Tatsuya Kubokawa

    (University of Tokyo)

Abstract

In this paper, we consider prediction for the exponential distribution with unknown location. For the most part, we treat the one-dimensional case and assume that the location parameter is restricted to an interval. The Bayesian predictive densities with respect to prior densities supported on the real line and the restricted space are compared under the Kullback–Leibler divergence. We first consider the case where the scale parameter is known. We obtain general dominance conditions and also minimaxity and admissibility results. Next, we treat the case of unknown scale. In this case, the location parameter is assumed to be less than a known constant and sufficient conditions for domination are obtained. Finally, we treat a multidimensional problem with known scale where the location parameter is restricted to a convex set. The performance of several Bayesian predictive densities is investigated through simulation. Some of the prediction methods are applied to real data.

Suggested Citation

  • Yasuyuki Hamura & Tatsuya Kubokawa, 2022. "Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 515-536, May.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:4:d:10.1007_s00184-021-00840-3
    DOI: 10.1007/s00184-021-00840-3
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    References listed on IDEAS

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    1. Komaki, Fumiyasu, 2015. "Simultaneous prediction for independent Poisson processes with different durations," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 35-48.
    2. Rahmath Manzil Juvairiyya & Parameshwaranpillai Anilkumar, 2018. "Estimation Of Stress-Strength Reliability For The Pareto Distribution Based On Upper Record Values," Statistica, Department of Statistics, University of Bologna, vol. 78(4), pages 397-409.
    3. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E. & Turcotte, Jean-Philippe, 2013. "Minimaxity in predictive density estimation with parametric constraints," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 382-397.
    4. Hartigan, J. A., 2004. "Uniform priors on convex sets improve risk," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 285-288, May.
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