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 $\widetilde{\theta }_{n}$, 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 $\widetilde{\theta }_{n}$. 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).