Strong Gaussian approximations with random multipliers

Conference paper

Fabian Mies
Springer Proceedings in Mathematics & Statistics, A. Steland, E. Rafajłowicz, N. Parolya, Stochastic Models, Statistics and Their Applications. SMSA 2024, vol. 499, Springer, 2024

DOI: 10.1007/978-3-031-96015-4_1

arXiv

Cite

APA Click to copy
Mies, F. (2024). Strong Gaussian approximations with random multipliers. In A. Steland, E. Rafajłowicz, & N. Parolya (Eds.), Stochastic Models, Statistics and Their Applications. SMSA 2024 (Vol. 499). Springer. https://doi.org/10.1007/978-3-031-96015-4_1

Chicago/Turabian Click to copy
Mies, Fabian. “Strong Gaussian Approximations with Random Multipliers.” In Stochastic Models, Statistics and Their Applications. SMSA 2024, edited by A. Steland, E. Rafajłowicz, and N. Parolya. Vol. 499. Springer Proceedings in Mathematics & Statistics. Springer, 2024.

MLA Click to copy
Mies, Fabian. “Strong Gaussian Approximations with Random Multipliers.” Stochastic Models, Statistics and Their Applications. SMSA 2024, edited by A. Steland et al., vol. 499, Springer, 2024, doi:10.1007/978-3-031-96015-4_1.

BibTeX Click to copy

@inproceedings{fabian2024a,
  title = {Strong Gaussian approximations with random multipliers},
  year = {2024},
  publisher = {Springer},
  series = {Springer Proceedings in Mathematics & Statistics},
  volume = {499},
  doi = {10.1007/978-3-031-96015-4_1},
  author = {Mies, Fabian},
  editor = {Steland, A. and Rafajłowicz, E. and Parolya, N.},
  booktitle = {Stochastic Models, Statistics and Their Applications. SMSA 2024}
}

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.