New asymptotic results in principal component analysis

Vladimir Koltchinskii, Karim Lounici

Let $X$ be a mean zero Gaussian random vector in a separable Hilbert space $\mathbb{H}$ with covariance operator $\Sigma :=\mathbb{E}(X\otimes X).$ Let $\Sigma ={\sum }_{r\ge 1}{\mu }_r{P}_r$ be the…