Quantitative limit theorems and bootstrap approximations for empirical spectral projectors

Jirak M, Wahl M (2022)
arXiv:2208.12871.

Preprint | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Jirak, Moritz; Wahl, MartinUniBi
Abstract / Bemerkung
Given finite i.i.d.~samples in a Hilbert space with zero mean and trace-class covariance operator $\Sigma$, the problem of recovering the spectral projectors of $\Sigma$ naturally arises in many applications. In this paper, we consider the problem of finding distributional approximations of the spectral projectors of the empirical covariance operator $\hat \Sigma$, and offer a dimension-free framework where the complexity is characterized by the so-called relative rank of $\Sigma$. In this setting, novel quantitative limit theorems and bootstrap approximations are presented subject only to mild conditions in terms of moments and spectral decay. In many cases, these even improve upon existing results in a Gaussian setting.
Erscheinungsjahr
2022
Zeitschriftentitel
arXiv:2208.12871
Page URI
https://pub.uni-bielefeld.de/record/2969758

Zitieren

Jirak M, Wahl M. Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. arXiv:2208.12871. 2022.
Jirak, M., & Wahl, M. (2022). Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. arXiv:2208.12871
Jirak, Moritz, and Wahl, Martin. 2022. “Quantitative limit theorems and bootstrap approximations for empirical spectral projectors”. arXiv:2208.12871.
Jirak, M., and Wahl, M. (2022). Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. arXiv:2208.12871.
Jirak, M., & Wahl, M., 2022. Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. arXiv:2208.12871.
M. Jirak and M. Wahl, “Quantitative limit theorems and bootstrap approximations for empirical spectral projectors”, arXiv:2208.12871, 2022.
Jirak, M., Wahl, M.: Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. arXiv:2208.12871. (2022).
Jirak, Moritz, and Wahl, Martin. “Quantitative limit theorems and bootstrap approximations for empirical spectral projectors”. arXiv:2208.12871 (2022).
Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Quellen

arXiv: 2208.12871

Suchen in

Google Scholar