Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency

This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted θ, for the Ornstein-Uhlenbeck process X: = { X_t, t≥ 0 } observed at high frequency. We provide an approximate minimum contrast estimator and an approximate maximum likelihood estimator of θ, namely θ˜n:=1/(2n∑i=1nXti2), and θˆn:=−∑i=1nXti−1(Xti−Xti−1)/(Δn∑i=1nXti−12), respectively, where t_i= iΔ _n, i= 0 , 1 , … , n, Δ _n→ 0. We provide Wasserstein bounds in the central limit theorem for θ˜ _n and θˆ _n.