  In this paper we derive martingale estimating functions for the
dimensionality parameter of a Bessel process based on the eigenfunctions of the
diffusion operator. Since a Bessel process is non-ergodic and the theory of
martingale estimating functions is developed for ergodic diffusions, we use the
space-time transformation of the Bessel process and formulate our results for a
modified Bessel process. We deduce consistency, asymptotic normality and
discuss optimality. It turns out that the martingale estimating function based
of the first eigenfunction of the modified Bessel process coincides with the
linear martingale estimating function for the Cox Ingersoll Ross process.
Furthermore, our results may also be applied to estimating the multiplicity
parameter of a one-dimensional Dunkl process.
