Minimax estimation for mixtures of Wishart distributions

Details Minimax estimation for mixtures of Wishart distributions Minimax estimation for mixtures of Wishart distributions

2012-03-15

arxiv.org/abs/1203.3342v1

Annals of Statistics 2011, Vol. 39, No. 6, 3417-3440

Mathematics

Statistics Theory

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

Scientific paper

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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