JSM 2005 - Toronto

Abstract #303413

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 64
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #303413
Title: A Generalized Maximum Likelihood Prior
Author(s): Anna Nicolaou*+ and Mihaela Aslan
Companies: University of Macedonia and Yale University
Address: 156 Egnatia str, Thessaloniki, AB, 54006, Greece
Keywords: Bayes estimate ; a-affine parameter ; maximum likelihood
Abstract:

The one-dimensional curved exponential family can be parametrized so it becomes a geodesic with respect to the a-connection geometry. The bias of the maximum likelihood estimate of the a-affine parameter determines a bias-adjusted estimate. We show its asymptotic risk differs negligibly from the asymptotic risk of the Bayes estimate that corresponds to the (1+a)/2 relatively invariant prior. The value a=-1 produces the maximum likelihood prior; its associated Bayes estimate is asymptotically equal to the maximum likelihood estimate of the -1-affine parameter, which is asymptotically unbiased. For a general family of distributions immersed into an a-flat manifold, the prior is induced by the tangential components of the asymptotic bias of the maximum likelihood estimate.

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