A0791
Title: Nonparametric bootstrap of high-dimensional sample covariance matrices
Authors: Holger Dette - Ruhr-Universitaet Bochum (Germany)
Angelika Rohde - University of Freiburg (Germany) [presenting]
Abstract: A new '$(m,mp/n)$ out of $(n,p)$ sampling-with-replacement bootstrap is introduced for eigenvalue statistics of high-dimensional sample covariance matrices based on $n$ independent $p$-dimensional random vectors. In the high-dimensional scenario $p/n\rightarrow c\in (0,\infty)$, this fully nonparametric and computationally tractable bootstrap is shown to consistently reproduce the empirical spectral measure if $m/n\rightarrow 0$. If $m^2/n\rightarrow 0$, it approximates correctly the distribution of linear spectral statistics. The crucial component is a suitably defined representative subpopulation condition, which is shown to be verified in a large variety of situations. The proofs are conducted under minimal moment requirements and incorporate delicate results on non-centered quadratic forms, combinatorial trace moments estimates as well as a conditional bootstrap martingale CLT which may be of independent interest.
