Journal article
Fabian Mies, Ansgar Steland
Bernoulli, vol. 29(4), 2023, pp. 3114-3140
Bernoulli, vol. 29(4), 2023, pp. 3114-3140
DOI:
10.3150/22-BEJ1577
arXiv
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APA
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Mies, F., & Steland, A. (2023). Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions. Bernoulli, 29(4), 3114–3140. https://doi.org/10.3150/22-BEJ1577
Chicago/Turabian
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Mies, Fabian, and Ansgar Steland. “Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions.” Bernoulli 29, no. 4 (2023): 3114–3140.
MLA
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Mies, Fabian, and Ansgar Steland. “Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions.” Bernoulli, vol. 29, no. 4, 2023, pp. 3114–40, doi:10.3150/22-BEJ1577.
BibTeX Click to copy
@article{mies2023a,
title = {Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions},
year = {2023},
issue = {4},
journal = {Bernoulli},
pages = {3114-3140},
volume = {29},
doi = {10.3150/22-BEJ1577},
author = {Mies, Fabian and Steland, Ansgar}
}
Gaussian couplings of partial sum processes are derived for the high-dimensional regime d=o(n1/3). The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities depend explicitly on the dimension and on a measure of nonstationarity, and are thus also applicable to arrays of random vectors. To enable high-dimensional statistical inference, a feasible Gaussian approximation scheme is proposed. Applications to sequential testing and change-point detection are described.
