Let be a stationary Gaussian process. We study two estimators of , namely , and , where , , and . We prove that the two estimators are strongly consistent and establish Berry-Esseen bounds for a central limit theorem involving and . We apply these results to asymptotically stationary Gaussian processes and estimate the drift parameter for Gaussian Ornstein-Uhlenbeck processes.
G. Kerchev and I. Nourdin were supported by the FNR grant APOGEe (R-AGR-3585-10) at Luxembourg University.
We would like to thank the referee for his/her careful readings, constructive remarks and useful suggestions.
"Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency." Electron. J. Statist. 16 (1) 636 - 670, 2022. https://doi.org/10.1214/21-EJS1967