Quantitative limit theorems and bootstrap approximations for empirical spectral projectors
Moritz Jirak,
Martin Wahl
Abstract:Given finite i.i.d. samples in a Hilbert space with zero mean and trace-class covariance operator $$\Sigma $$
Σ
, the problem of recovering the spectral projectors of $$\Sigma $$
Σ
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 $${\hat{\Sigma }}$$
Σ
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