OPTIMIZATION OF THE GAUSSIAN AND JEFFREYS POWER PRIORS WITH EMPHASIS ON THE CANONICAL PARAMETERS IN THE EXPONENTIAL FAMILY

• Ogasawara Haruhiko

  Otaru University of Commerce

Abstract

Optimal powers of the Gaussian and Jeffreys priors are obtained so that they minimize the asymptotic mean square error of the linear predictor and the sum of the asymptotic mean square errors of associated parameter estimators. Conditions that the summarized mean square errors using powers of the priors are smaller than those by maximum likelihood are given. In the case of a scalar canonical parameter in the exponential family, a matching prior for the Jeffreys power prior is found, where the Wald confidence interval has second-order accurate coverage. The results are numerically illustrated using the categorical distribution and logistic regression.

Journal

• Behaviormetrika

  Behaviormetrika 41 (2), 195-223, 2014

  The Behaviormetric Society

Keywords

• Gaussian prior
• Jeffreys prior
• weighted score
• penalized likelihood
• mean square error
• asymptotic cumulants
• Cornish-Fisher expansion

Details

• CRID: 1390001205112356224
• NII Article ID: 130004699267
• NII Book ID: AA00095330
• DOI: 10.2333/bhmk.41.195
• ISSN: 13496964
• ISSN: 03857417
• Web Site: http://hdl.handle.net/10252/5382
• Web Site: http://link.springer.com/content/pdf/10.2333/bhmk.41.195.pdf
• Web Site: http://link.springer.com/article/10.2333/bhmk.41.195/fulltext.html
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed