Saddlepoint condition on a predictor to reconfirm the need for the assumption of a prior distribution

Saddlepoint conditions on a predictor are introduced and developed to reconfirm the need for the assumption of a prior distribution in constructing a useful inferential procedure. A condition yields that the predictor induced from the maximum likelihood estimator is the worst under a loss, while the...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2011-05, Vol.141 (5), p.1990-2000
Main Authors: Yanagimoto, Takemi, Ohnishi, Toshio
Format: Article
Language:English
Subjects:
Canonical parameter
Decision theory
DIC
e-mixture
Exact sciences and technology
General topics
Logarithmic divergence
Marginal likelihood
Mathematics
Maximum likelihood estimator
Posterior mean
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary:Saddlepoint conditions on a predictor are introduced and developed to reconfirm the need for the assumption of a prior distribution in constructing a useful inferential procedure. A condition yields that the predictor induced from the maximum likelihood estimator is the worst under a loss, while the predictor induced from a suitable posterior mean is the best. This result indicates the promising role of Bayesian criteria, such as the deviance information criterion (DIC). As an implication, we critique the conventional empirical Bayes method because of its partial assumption of a prior distribution.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2010.12.011