文章基本信息

标题：Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency
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作者：Soukaina Douissi ; Khalifa Es-Sebaiy ; George Kerchev 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2022
卷号：16
期号：1
页码：636-670
DOI：10.1214/21-EJS1967
语种：English
出版社：Institute of Mathematical Statistics
摘要：Let Z:={Zt,t≥0} be a stationary Gaussian process. We study two estimators of E[Z02], namely fˆT(Z):=1 T ∫0TZt2dt, and f˜n(Z):=1 n ∑i=1nZti2, where ti=iΔn, i=0,1,…,n, Δn→0 and Tn:=nΔn→∞. We prove that the two estimators are strongly consistent and establish Berry-Esseen bounds for a central limit theorem involving fˆT(Z) and f˜n(Z). We apply these results to asymptotically stationary Gaussian processes and estimate the drift parameter for Gaussian Ornstein-Uhlenbeck processes.
关键词：60F05;60G10;60G15;62F12;62M09;continuous-time observation;High frequency data;Parameter estimation;rate of normal convergence of the estimators;Stationary Gaussian processes;strong consistency