Quotation Hornik, Kurt, Grün, Bettina. Forthcoming. On maximum likelihood estimation of the concentration parameter of von Mises-Fisher distributions. Computational Statistics. 29 (5), 945-957.


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Abstract

Maximum likelihood estimation of the concentration parameter of von Mises-Fisher distributions involves inverting the ratio Rν=Iν+1/Iν of modified Bessel functions and computational methods are required to invert these functions using approximative or iterative algorithms. In this paper we use Amos-type bounds for Rν to deduce sharper bounds for the inverse function, determine the approximation error of these bounds, and use these to propose a new approximation for which the error tends to zero when the inverse of Rν is evaluated at values tending to 1 (from the left). We show that previously introduced rational bounds for Rν which are invertible using quadratic equations cannot be used to improve these bounds.

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Publication's profile

Affiliation WU
Type of publication Journal article
Journal Computational Statistics
Citation Index SCI
WU-Journal-Rating new FIN-A
Language English
Title On maximum likelihood estimation of the concentration parameter of von Mises-Fisher distributions.
Volume 29
Number 5
Year 2014
Page from 945
Page to 957
Reviewed? Y
URL http://epub.wu.ac.at/3669/
DOI 10.1007/s00180-013-0471-0
Open Access Y
Open Access Link https://doi.org/10.1007/s00180-013-0471-0

Associations

People
Hornik, Kurt (Details)
Grün, Bettina (Details)
Organization
Institute for Statistics and Mathematics IN (Details)
Research Institute for Computational Methods FI (Details)
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