Sequential maximum likelihood estimation for reflected Ornstein–Uhlenbeck processes

Abstract

The paper studies the properties of a sequential maximum likelihood estimator of the drift parameter in a one dimensional reflected Ornstein–Uhlenbeck process. We observe the process until the observed Fisher information reaches a specified precision level. We derive the explicit formulas for the sequential estimator and its mean squared error. The estimator is shown to be unbiased and uniformly normally distributed. A simulation study is conducted to assess the performance of the estimator compared with the ordinary maximum likelihood estimator.