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

Takemi Yanagimoto, Toshio Ohnishi

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

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.

Original language English 1990-2000 11 Journal of Statistical Planning and Inference 141 5 https://doi.org/10.1016/j.jspi.2010.12.011 Published - May 1 2011

### Fingerprint

Prior distribution
Maximum likelihood
Predictors
Empirical Bayes Method
Deviance Information Criterion
Posterior Mean
Maximum Likelihood Estimator
Partial

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty
• Applied Mathematics

### Cite this

In: Journal of Statistical Planning and Inference, Vol. 141, No. 5, 01.05.2011, p. 1990-2000.

Research output: Contribution to journalArticle

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