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- W4287330068 abstract "Let $Z:={Z_t,tgeq0}$ be a stationary Gaussian process. We study two estimators of $mathbb{E}[Z_0^2]$, namely $widehat{f}_T(Z):= frac{1}{T} int_{0}^{T} Z_{t}^{2}dt$, and $widetilde{f}_n(Z) :=frac{1}{n} sum_{i =1}^{n} Z_{t_{i}}^{2}$, where $ t_{i} = i Delta_{n}$, $ i=0,1,ldots, n $, $Delta_{n}rightarrow 0$ and $ T_{n} := n Delta_{n}rightarrow infty$. We prove that the two estimators are strongly consistent and establish Berry-Esseen bounds for a central limit theorem involving $widehat{f}_T(Z)$ and $widetilde{f}_n(Z)$. We apply these results to asymptotically stationary Gaussian processes and estimate the drift parameter for Gaussian Ornstein-Uhlenbeck processes." @default.
- W4287330068 created "2022-07-25" @default.
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- W4287330068 date "2021-02-09" @default.
- W4287330068 modified "2023-10-14" @default.
- W4287330068 title "Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency" @default.
- W4287330068 doi "https://doi.org/10.48550/arxiv.2102.04810" @default.
- W4287330068 hasPublicationYear "2021" @default.
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