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 - GrĂ¼n, Bettina
ER -