# Concentration inequalities and moment bounds for sample covariance operators

@article{Koltchinskii2014ConcentrationIA,
title={Concentration inequalities and moment bounds for sample covariance operators},
journal={Bernoulli},
year={2014},
volume={23},
pages={110-133}
}
• Published 10 May 2014
• Mathematics
• Bernoulli
Let $X,X_1,\dots, X_n,\dots$ be i.i.d. centered Gaussian random variables in a separable Banach space $E$ with covariance operator $\Sigma:$ $$\Sigma:E^{\ast}\mapsto E,\ \ \Sigma u = {\mathbb E}\langle X,u\rangle, u\in E^{\ast}.$$ The sample covariance operator $\hat \Sigma:E^{\ast}\mapsto E$ is defined as $$\hat \Sigma u := n^{-1}\sum_{j=1}^n \langle X_j,u\rangle X_j, u\in E^{\ast}.$$ The goal of the paper is to obtain concentration inequalities and expectation bounds for the operator norm…
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