Optimal Berry-Esseen bound for an estimator of parameter in the Ornstein-Uhlenbeck process

This paper is concerned with the study of the rate of central limit theorem for the maximum likelihood estimator (theta) over bar (T), of the unknown parameter theta > 0, based on the observation X = {X-t, 0 <= t <= T}, occurring in the drift coefficient of an Ornstein-Uhlenbeck process dX(t) = -theta X(t)dt + dW(t), X-0 = 0 for 0 <= t <= T, where {W-t, t >= 0} is a standard Brownian motion. The tool we use is an Edgeworth expansion with an explicitly expressed remainder. We prove that upper and lower bounds, obtained by controlling the remainder term, give an optimal rate 1/root T. in Kolmogorov distance for normal approximation of (theta) over bar (T). (C) 2017 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.