Abstract

We offer a bootstrap procedure for building sharp confidence sets for the projectors of a covariance matrix from the given sample. This procedure could be applied for small or moderate sample size and large dimension of observations. The main result states the validity of the proposed procedure for finite samples with an explicit error bound of bootstrap approximation. This bound involves some new sharp results on Gaussian comparison and Gaussian anti-concentration in high dimensions. These are the joint results with V.Spokoiny (WIAS, Berlin).