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MINIMAX ESTIMATION FOR MIXTURES OF WISHART DISTRIBUTIONS

Authors
Haff, L. R.Kim, P. T.Koo, J. -Y.Richards, D. St P.
Issue Date
12월-2011
Publisher
INST MATHEMATICAL STATISTICS
Keywords
Deconvolution; Harish-Chandra c-function; Helgason-Fourier transform; Laplace-Beltrami operator; optimal rate; Sobolev ellipsoid; stochastic volatility
Citation
ANNALS OF STATISTICS, v.39, no.6, pp.3417 - 3440
Indexed
SCIE
SCOPUS
Journal Title
ANNALS OF STATISTICS
Volume
39
Number
6
Start Page
3417
End Page
3440
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/110968
DOI
10.1214/11-AOS951
ISSN
0090-5364
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.
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