Angular Gaussian and Cauchy estimation

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• 作者：Auderset ; Claude ; Mazza ; Christian ; Ruh ; Ernst A.
• 关键词：62H11 ; 62H12 ; 62F10 ; Multivariate Cauchy ; Angular Gaussian ; Directional and shape analysis ; Maximum likelihood ; Differential geometry ; Equivariance ; Geodesics ; Symmetric spaces
• 刊名：Journal of Multivariate Analysis
• 出版年：2005
• 期刊代码：77_0047259x
• 类别：mt
• 出版时间：March, 2005
• 卷：93
• 期：1
• 页码：180-197
• 文件大小：312 K

摘要

This paper proposes a unified treatment of maximum likelihood estimates of angular Gaussian and multivariate Cauchy distributions in both the real and the complex case. The complex case is relevant in shape analysis. We describe in full generality the set of maxima of the corresponding log-likelihood functions with respect to an arbitrary probability measure. Our tools are the convexity of log-likelihood functions and their behaviour at infinity.