Title: Hybrid estimators for ergodic diffusion processes based on thinned data
Authors: Masayuki Uchida - Osaka University (Japan) [presenting]
Abstract: Hybrid estimation is considered for both drift and diffusion coefficient parameters for discretely observed ergodic diffusion processes. In order to get the maximum likelihood type estimator, it is crucial to choose a suitable initial estimator for optimization of the quasi likelihood function. From a computational point of view, an initial Bayes type estimator of the diffusion coefficient parameter is given by using reduced data obtained from full data, and an initial Bayes type estimator of the drift parameter is obtained by using thinned data out of full data. The adaptive maximum likelihood type estimator with the initial Bayes type estimator, which is called hybrid estimator, is proposed. The asymptotic properties of the initial Bayes type estimators are proved. Moreover, it is shown that the hybrid estimators based on the initial Bayes type estimators have asymptotic normality and convergence of moments. In order to investigate asymptotic performance of the proposed estimators, we give a concrete example and simulation results.