Concentration Inequalities and Moment Bounds for Sample Covariance Operators

Vladimir Koltchinskii, Karim Lounici

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 $\Sigma :$ $$ Σ:E^{\ast}\mapsto E,\ \ Σu = {\mathbb E}\…