High-dimensional regression with unknown variance

TL;DR

This paper reviews recent advances in high-dimensional sparse linear regression with unknown variance, focusing on non-asymptotic analysis, practical procedures, and comparing tuning schemes for the Lasso estimator across various sparsity settings.

Contribution

It provides a comprehensive review of recent results for high-dimensional regression with unknown variance, covering multiple sparsity types and emphasizing practical, non-asymptotic methods.

Findings

Comparison of three Lasso tuning schemes shows practical differences.

Non-asymptotic analyses provide theoretical guarantees.

Numerical study illustrates performance across models.

Abstract

We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is put on non-asymptotic analyses and feasible procedures. In addition, a small numerical study compares the practical performance of three schemes for tuning the Lasso estimator and some references are collected for some more general models, including multivariate regression and nonparametric regression.