Berry–Esseen Asymptotics for Pearson Diffusions

Abstract

Using Malliavin calculus along with Stein’s equation, the chapter shows that the distribution of the maximum likelihood estimator of the drift parameter in the Pearson diffusion process observed over [0, T] converges to the standard normal distribution with an uniform error rate of the order O(T ^−1∕2). Then based on discrete observations, it obtains martingale estimation function estimators and studies their rate of weak convergence to normal distribution.