Minimax estimation for mixtures of Wishart distributions

Abstract

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.

Published in at http://dx.doi.org/10.1214/11-AOS951 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy--Widom limits and rates of convergence
• Wishart distributions for decomposable graphs

Cited by in corpus (3)

• A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications
• Normal approximations for the multivariate inverse Gaussian distribution and asymmetric kernel smoothing on $d$-dimensional half-spaces
• On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models