Journal article
Fabian Mies
arXiv, 2412.14346 , 2024
arXiv, 2412.14346 , 2024
arXiv
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APA
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Mies, F. (2024). Strong Gaussian approximations with random multipliers. ArXiv, 2412.14346 . https://doi.org/10.48550/arXiv.2412.14346
Chicago/Turabian
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Mies, Fabian. “Strong Gaussian Approximations with Random Multipliers.” arXiv 2412.14346 (2024).
MLA
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Mies, Fabian. “Strong Gaussian Approximations with Random Multipliers.” ArXiv, vol. 2412.14346 , 2024, doi:10.48550/arXiv.2412.14346.
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@article{fabian2024a,
title = {Strong Gaussian approximations with random multipliers},
year = {2024},
journal = {arXiv},
volume = {2412.14346 },
doi = {10.48550/arXiv.2412.14346},
author = {Mies, Fabian}
}
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object.
Instead, suitable distributional approximations can be used, where the approximating object is not constant, but a sequence as well. We extend Gaussian approximation results for the partial sum process by allowing each summand to be multiplied by a data-dependent matrix. The results allow for serial dependence of the data, and for high-dimensionality of both the data and the multipliers. In the finite-dimensional and locally-stationary setting, we obtain a functional central limit theorem as a direct consequence. An application to sequential testing in non-stationary environments is described.
Instead, suitable distributional approximations can be used, where the approximating object is not constant, but a sequence as well. We extend Gaussian approximation results for the partial sum process by allowing each summand to be multiplied by a data-dependent matrix. The results allow for serial dependence of the data, and for high-dimensionality of both the data and the multipliers. In the finite-dimensional and locally-stationary setting, we obtain a functional central limit theorem as a direct consequence. An application to sequential testing in non-stationary environments is described.