Squared-Norm Empirical Process in Banach Space
Probability
2013-12-05 v1 Statistics Theory
Statistics Theory
Abstract
This note extends a recent result of Mendelson on the supremum of a quadratic process to squared norms of functions taking values in a Banach space. Our method of proof is a reduction by a symmetrization argument and observation about the subadditivity of the generic chaining functional. We provide an application to the supremum of a linear process in the sample covariance matrix indexed by finite rank, positive definite matrices.
Cite
@article{arxiv.1312.1005,
title = {Squared-Norm Empirical Process in Banach Space},
author = {Vincent Q. Vu and Jing Lei},
journal= {arXiv preprint arXiv:1312.1005},
year = {2013}
}
Comments
This note was first written in 2012 and a version has been available on the first author's website. It is now posted on arXiv to provide a universal identifier for citations elsewhere. It is not intended for publication in its current form, but a revision incorporating later work will be posted separately