Year: 2020
Type: preprint
Abstract: Much of the theory for the lasso in the linear model $Y = X β^* + \varepsilon$ hinges on the quantity $2 \| X^\top \varepsilon \|_{\infty} / n$, which we call the lasso's effective noise. Among other things, the effective noise plays an important role in finite-sample bounds for the lasso, the calibration of the lasso's tuning parameter, and inference on the parameter vector $β^*$. In this paper, we develop a bootstrap-based estimator of the quantiles of the effective noise. The estimator is fully data-driven, that is, does not require any additional tuning parameters. We equip our estimator with finite-sample guarantees and apply it to tuning parameter calibration for the lasso and to high-dimensional inference on the parameter vector $β^*$.
Source: arXiv (Cornell University)
Authors: Lederer, Johannes, Vogt, Michael
Institutions: Ruhr University Bochum, University of Bonn, Universität Ulm
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3019554361