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

Yasuyuki Hamura and Tatsuya Kubokawa ()
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Tatsuya Kubokawa: University of Tokyo

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 4, No 5, 515-536

Abstract: 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.

Keywords: Admissibility; Bayesian predictive density estimation; Dominance; Exponential distribution; Minimaxity; Restricted parameter space (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00840-3

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