Open Access
December 2011 Minimax estimation for mixtures of Wishart distributions
L. R. Haff, P. T. Kim, J.-Y. Koo, D. St. P. Richards
Ann. Statist. 39(6): 3417-3440 (December 2011). DOI: 10.1214/11-AOS951


The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been written on this subject, and more recently there has been considerable interest in high-dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. With the availability of modern data acquisition capabilities, smoothing or nonparametric techniques are required that go beyond those applicable only to data arising in Euclidean spaces. Accordingly, we present a Fourier method of minimax Wishart mixture density estimation on the space of positive definite symmetric matrices.


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L. R. Haff. P. T. Kim. J.-Y. Koo. D. St. P. Richards. "Minimax estimation for mixtures of Wishart distributions." Ann. Statist. 39 (6) 3417 - 3440, December 2011.


Published: December 2011
First available in Project Euclid: 5 March 2012

zbMATH: 1246.62202
MathSciNet: MR3012414
Digital Object Identifier: 10.1214/11-AOS951

Primary: 62G20
Secondary: 65R32

Keywords: Deconvolution , Harish–Chandra c-function , Helgason–Fourier transform , Laplace–Beltrami operator , optimal rate , Sobolev ellipsoid , stochastic volatility

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 6 • December 2011
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