We introduce a new '\((m,mp/n)\) out of \((n,p)\)'-sampling with replacement bootstrap for linear spectral statistics of high-dimensional sample covariance matrices based on \(n\) independent \(p\)-dimensional random vectors. For a large class of population covariance matrices satisfying the so-called representative subpopulation condition, this fully nonparametric bootstrap is shown to be consistent in the high-dimensional scenario \(p/n\rightarrow c\in (0,\infty)\) iff \(m^2/n\rightarrow 0\). This is in sharp contrast to the inconsistency of the classical sampling with replacement bootstrap in the high-dimensional scenario. The talk is based on a joint work with Holger Dette (Ruhr-Universität Bochum).