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Angular Gaussian and Cauchy estimation

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  • Auderset, Claude
  • Mazza, Christian
  • Ruh, Ernst A.

Abstract

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.

Suggested Citation

  • Auderset, Claude & Mazza, Christian & Ruh, Ernst A., 2005. "Angular Gaussian and Cauchy estimation," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 180-197, March.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:1:p:180-197
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    References listed on IDEAS

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    1. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
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    Cited by:

    1. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    2. Ciobotaru, Corina & Mazza, Christian, 2022. "Consistency and asymptotic normality of M-estimates of scatter on Grassmann manifolds," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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