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

TL;DR

This paper investigates non-asymptotic bounds for high-dimensional generalized linear model estimators with L1 penalty, demonstrating bounds without traditional chaining or peeling techniques.

Contribution

It provides a novel approach to deriving non-asymptotic bounds for penalized estimators in high-dimensional GLMs without using chaining or peeling methods.

Findings

Non-asymptotic bounds are achievable without chaining.

The approach applies to models with highly correlated design matrices.

Results contribute to understanding estimator behavior in high-dimensional settings.

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.