Minimum Hellinger Distance Estimation for Discretely Observed Stochastic Processes Using Recursive Kernel Density Estimator

The paper deals with the estimation of the parameters of stochastic processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This method is based on the minimization of the Hellinger distance between the density of the invariant distribution of the stochastic process and a nonparametric estimator of this density. We give conditions which ensure the existence of an invariant measure that admits density with respect to the Lebesgue measure and the strong mixing property with geometric rate for the stochastic process. Under these conditions, using the recursive kernel density estimator of the invariant density of the stochastic process, we construct the minimum Hellinger distance estimator of the parameters. As in the nonrecursive kernel density case, the minimum Hellinger distance estimator obtained using the recursive kernel density estimator is consistent and asymptotically normal. Simulation results show that the minimum Hellinger distance estimator obtained with recursive kernel density estimator is slightly better than that obtained with a nonrecursive kernel density estimator in terms of standard deviation or standard error.