TY  - JOUR
TI  - On maximum likelihood estimation of the concentration parameter of von Mises-Fisher distributions.
AB  - 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.
DO  - 10.1007/s00180-013-0471-0
SP  - 945
EP  - 957
UR  - http://epub.wu.ac.at/3669/
PY  - 2014-01-01
JO  - Computational Statistics
AU  - Hornik, Kurt 
AU  - Grün, Bettina 
ER -