MINIMAX ESTIMATION FOR MIXTURES OF WISHART DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Haff, L. R.; Kim, P. T.; Koo, J. -Y.; Richards, D. St P.
• 署名单位: University of California System; University of California San Diego; University of Guelph; Korea University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS951
• 发表日期: 2011
• 页码: 3417-3440
• 关键词: multivariate stochastic volatility; empirical bayes estimation; nonparametric deconvolution; COVARIANCE-MATRIX; Optimal Rates; CONVERGENCE

摘要

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.