Electronic Journal of Statistics

Bernstein-von Mises theorems for functionals of the covariance matrix

Chao Gao and Harrison H. Zhou

Full-text: Open access

Abstract

We provide a general theoretical framework to derive Bernstein-von Mises theorems for functionals of the covariance matrix and its inverse. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including entries of covariance matrix, entries of precision matrix, quadratic forms, log-determinant, eigenvalues in the Bayesian Gaussian covariance/precision matrix estimation setting, as well as for Bayesian linear and quadratic discriminant analysis.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 1751-1806.

Dates
Received: December 2014
First available in Project Euclid: 18 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1468849963

Digital Object Identifier
doi:10.1214/15-EJS1048

Mathematical Reviews number (MathSciNet)
MR3522660

Zentralblatt MATH identifier
1346.62059

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties

Keywords
Bernstein-von Mises theorem Bayes nonparametrics covariance matrix

Citation

Gao, Chao; Zhou, Harrison H. Bernstein-von Mises theorems for functionals of the covariance matrix. Electron. J. Statist. 10 (2016), no. 2, 1751--1806. doi:10.1214/15-EJS1048. https://projecteuclid.org/euclid.ejs/1468849963


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