Improved Berry-Esseen bounds for parameter estimation of a fractional Ornstein-Uhlenbeck process observed at high frequency

This paper deals with parameter estimation of the drift coefficient, denoted θ, for a fractional Ornstein-Uhlenbeck process observed at high frequency. Specifically, we provide an estimator of θ, namely ₍, using the second moment method. We develop some novel estimates to derive an explicit Berry–Esseen bound in the Wasserstein distance for the normal approximation of ₍. Moreover, we prove that our estimate is strictly sharper than the one obtained in Douissi et al. (Electron. J. Stat. 16 (1): 636–670, 2022).