High-dimensional regression with unknown variance

By Christophe Giraud, Sylvie Huet, Nicolas Verzelen. 2011

64 citations recorded by the source corpus.

We review recent results for high-dimensional sparse linear re- gression 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 nonasymptotic analyses and feasible pro- cedures. In addition, a small numerical study compares the practical perfor- mance of three schemes for tuning the lasso estimator and some references are collected for some more general models, including multivariate regres- sion and nonparametric regression.

Subfields: Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/42ad99afe8d841c4904d8b73d375d80f3ea79170

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Statistics and Probability

Citations in the corpus

Linear Hypothesis Testing in Dense High-Dimensional Linear Models (2016, background): “This topic received special attention, cf. Giraud et al. (2012) and the references therein.”
The Partial Linear Model in High Dimensions (2013, background): “We advise the reader to Belloni et al. (2011) and Giraud et al. (2012), where possible approaches for dealing with the unknown variance are extensively discussed.”
Pivotal estimation via square-root Lasso in nonparametric regression (2011, unknown): “A comprehensive review is given in [30].”
A Critical Review of LASSO and Its Derivatives for Variable Selection Under Dependence Among Covariates (2020, background): “It seems the LASSO tries to recover the set S but, due to the presence of spurious correlations, this chooses randomly between two highly correlated important covariates.”
Robust Subspace Clustering (2013, background): “In recent years, there has been much progress on this issue in the sparse regression literature; see [11, 19, 24, 48, 49] and references therein.”
Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization (2012, background): “Variance estimation in high-dimensional linear regression with Gaussian errors continues to be a topic of active research, with several significant advances made very recently [26].”