Sharper dimension-free bounds on the Frobenius distance between sample covariance and its expectation

Nikita Puchkin, Fedor Noskov, Vladimir Spokoiny

We study properties of a sample covariance estimate $\hat{\Sigma }$ given a finite sample of $n$ i.i.d. centered random elements in ${\mathbb{R}}^d$ with the covariance matrix $\Sigma$. We derive di…