Minimaxity in predictive density estimation with parametric constraints

This paper is concerned with estimation of a predictive density with parametric constraints under Kullback–Leibler loss. When an invariance structure is embedded in the problem, general and unified conditions for the minimaxity of the best equivariant predictive density estimator are derived. These...

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Bibliographic Details
Published in:Journal of multivariate analysis 2013-04, Vol.116, p.382-397
Main Authors: Kubokawa, Tatsuya, Marchand, Éric, Strawderman, William E., Turcotte, Jean-Philippe
Format: Article
Language:English
Subjects:
Bayes estimators
Bayesian analysis
Decision theory
Density
Dominance
Invariance
Kullback–Leibler loss
Location family
Location–scale family
Mathematical models
Minimaxity
Order restriction
Parameter estimation
Predictive density
Restricted parameter space
Scale family
Studies
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Summary:This paper is concerned with estimation of a predictive density with parametric constraints under Kullback–Leibler loss. When an invariance structure is embedded in the problem, general and unified conditions for the minimaxity of the best equivariant predictive density estimator are derived. These conditions are applied to check minimaxity in various restricted parameter spaces in location and/or scale families. Further, it is shown that the generalized Bayes estimator against the uniform prior over the restricted space is minimax and dominates the best equivariant estimator in a location family when the parameter is restricted to an interval of the form [a0,∞). Similar findings are obtained for scale parameter families. Finally, the presentation is accompanied by various observations and illustrations, such as normal, exponential location, and gamma model examples.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2013.01.001