Adaptive Bayes Estimators and Hybrid Estimators for Small Diffusion Processes Based on Sampled Data

Abstract

We study adaptive Bayes type estimation and hybrid type estimation of both drift and volatility parameters for small diffusion processes from discrete observations. By applying adaptive maximum likelihood type estimation for small diffusion processes to the Bayesian method and by using the polynomial type large deviation inequality for the statistical random field and Ibragimov-Has’minskii-Kutoyants program, the adaptive Bayes type estimators and hybrid type estimators are obtained and we show that they have asymptotic normality and convergence of moments.