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

Sara A. van de Geer

doi:10.1214/074921707000000319

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

Statistics Theory 2007-09-12 v1 Statistics Theory

Authors: Sara A. van de Geer

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

non-asymptotic bounds generalized linear models highly correlated design penalized empirical risk minimization l1 penalty

Cite

@article{arxiv.0709.0844,
  title  = {On non-asymptotic bounds for estimation in generalized linear models with highly correlated design},
  author = {Sara A. van de Geer},
  journal= {arXiv preprint arXiv:0709.0844},
  year   = {2007}
}

Comments

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)

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

Abstract

Keywords

Cite

Comments

Related papers