The Annals of Statistics

Wald Lecture: On the Bernstein-von Mises theorem with infinite-dimensional parameters

David Freedman

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Abstract

If there are many independent, identically distributed observations governed by a smooth, finite-dimensional statistical model, the Bayes estimate and the maximum likelihood estimate will be close. Furthermore, the posterior distribution of the parameter vector around the posterior mean will be close to the distribution of the maximum likelihood estimate around truth. Thus, Bayesian confidence sets have good frequentist coverage properties, and conversely. However, even for the simplest infinite-dimensional models, such results do not hold. The object here is to give some examples.

Article information

Source
Ann. Statist. Volume 27, Number 4 (1999), 1119-1141.

Dates
First available in Project Euclid: 4 April 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1017938917

Digital Object Identifier
doi:10.1214/aos/1017938917

Mathematical Reviews number (MathSciNet)
MR1740119

Zentralblatt MATH identifier
0957.62002

Subjects
Primary: 62A15
Secondary: 62C15: Admissibility

Keywords
Asymptotic confidence sets Bayesian inference consistency Gaussian priors

Citation

Freedman, David. Wald Lecture: On the Bernstein-von Mises theorem with infinite-dimensional parameters. Ann. Statist. 27 (1999), no. 4, 1119--1141. doi:10.1214/aos/1017938917. http://projecteuclid.org/euclid.aos/1017938917.


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