The Annals of Statistics

Maximum Likelihood Estimators for the Matrix Von Mises-Fisher and Bingham Distributions

P. E. Jupp and K. V. Mardia

Full-text: Open access

Abstract

It has been conjectured by Khatri and Mardia that with probability one MLEs for the parameters of the von Mises-Fisher matrix distribution exist and are unique. We prove that, except for small sample sizes, this conjecture is true, both in the case where the parameter matrix has known rank and in the unrestricted case. The corresponding result for the matrix Bingham distribution is proven also.

Article information

Source
Ann. Statist., Volume 7, Number 3 (1979), 599-606.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344681

Digital Object Identifier
doi:10.1214/aos/1176344681

Mathematical Reviews number (MathSciNet)
MR527495

Zentralblatt MATH identifier
0406.62012

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62F05: Asymptotic properties of tests

Keywords
Maximum likelihood estimator von Mises-Fisher matrix distribution Bingham matrix distribution exponential family

Citation

Jupp, P. E.; Mardia, K. V. Maximum Likelihood Estimators for the Matrix Von Mises-Fisher and Bingham Distributions. Ann. Statist. 7 (1979), no. 3, 599--606. doi:10.1214/aos/1176344681. https://projecteuclid.org/euclid.aos/1176344681


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