Quantitative limit theorems and bootstrap approximations for empirical spectral projectors

Jirak M, Wahl M (2024)
Probability Theory and Related Fields.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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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.
Stichworte
Covariance operator; Principal components analysis; Spectral projector; Normal approximation; Bootstrap; Relative rank; Relative perturbation; theory
Erscheinungsjahr
2024
Zeitschriftentitel
Probability Theory and Related Fields
ISSN
0178-8051
eISSN
1432-2064
Page URI
https://pub.uni-bielefeld.de/record/2969758

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Jirak M, Wahl M. Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. Probability Theory and Related Fields. 2024.
Jirak, M., & Wahl, M. (2024). Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-024-01290-4
Jirak, Moritz, and Wahl, Martin. 2024. “Quantitative limit theorems and bootstrap approximations for empirical spectral projectors”. Probability Theory and Related Fields.
Jirak, M., and Wahl, M. (2024). Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. Probability Theory and Related Fields.
Jirak, M., & Wahl, M., 2024. Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. Probability Theory and Related Fields.
M. Jirak and M. Wahl, “Quantitative limit theorems and bootstrap approximations for empirical spectral projectors”, Probability Theory and Related Fields, 2024.
Jirak, M., Wahl, M.: Quantitative limit theorems and bootstrap approximations for empirical spectral projectors. Probability Theory and Related Fields. (2024).
Jirak, Moritz, and Wahl, Martin. “Quantitative limit theorems and bootstrap approximations for empirical spectral projectors”. Probability Theory and Related Fields (2024).
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arXiv: 2208.12871

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