Quantitative limit theorems and bootstrap approximations for empirical spectral projectors

• Published in: Probability theory and related fields Vol. 190; no. 1-2; pp. 119 - 177
• Main Authors: Jirak, Moritz, Wahl, Martin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2024; Springer Nature B.V
• Subjects: Approximation; Covariance; Economics; Eigenvalues; Finance; Hilbert space; Inequality; Insurance; Management; Mathematical and Computational Biology; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Projectors; Quantitative Finance; Random variables; Statistics for Business; Theorems; Theoretical; Normal approximation; Relative perturbation theory; Covariance operator; 62G09; 47A55; Principal components analysis; Bootstrap; Relative rank; 60F05; Spectral projector; 62H25

Given finite i.i.d. samples in a Hilbert space with zero mean and trace-class covariance operator Σ , the problem of recovering the spectral projectors of Σ naturally arises in many applications. In this paper, we consider the problem of finding distributional approximations of the spectral projecto...