Hybrid estimation for ergodic diffusion processes based on noisy discrete observations

Abstract

We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators. In order to select proper initial values for optimisation of the quasi likelihood function of ergodic diffusion processes with noisy observations, we construct the initial Bayes type estimator based on the local means of the noisy observations. The asymptotic properties of the initial Bayes type estimators and the hybrid multi-step estimators with the initial Bayes type estimators are shown, and a concrete example and the simulation results are given.

Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise

“…In particular, the hybrid type estimators with initial Bayes-type estimators are considered for diffusion type processes, see Kamatani and Uchida (2015); Kaino and Uchida (2018a,b), and references therein. Moreover, as an application of the Bayes-type estimation proposed in this paper, Kaino et al (2018) study the hybrid estimators with initial Bayes-type estimators for our ergodic diffusion plus noise model and give an example and simulation results of the hybrid estimator.…”