Optimal estimation for continuous state branching processes with discrete sampling

This paper is concerned with estimation of the drift parameter in a Glass of continuous state branching processes by use of the estimating function theory (Heyde, 1992, J. Statist. Plann. Inference 33, 121-129). The main interests are to develop a method of estimating the parameter in case when only discrete sampling is available. For this purpose, a discretized quasi-score function is introduced and a discretized optimal estimator derived therefrom is obtained. Large-sample properties of the discretized optimal estimator are established. Finally, two examples of continuous state branching processes are given. (C) 1998 Elsevier Science B.V. All rights reserved.