Minimax estimation for mixtures of Wishart distributions

TL;DR

This paper introduces a Fourier-based minimax method for estimating mixture densities of Wishart distributions on the space of positive definite matrices, addressing challenges in high-dimensional multivariate data analysis.

Contribution

It proposes a novel nonparametric estimation technique specifically designed for Wishart mixtures on positive definite matrices, extending existing methods beyond Euclidean spaces.

Findings

Developed a Fourier-based minimax estimator for Wishart mixtures

Addresses high-dimensional dependence structures in multivariate data

Provides a new tool for nonparametric density estimation on matrix spaces

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.