On non-asymptotic bounds for estimation in generalized linear models with highly correlated design

Abstract

We study a high-dimensional generalized linear model and penalized empirical risk minimization with ${\ell }_1$ penalty. Our aim is to provide a non-trivial illustration that non-asymptotic bounds for the estimator can be obtained without relying on the chaining technique and/or the peeling device.

Published at http://dx.doi.org/10.1214/074921707000000319 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)