A0168
Title: Estimating the lasso's effective noise
Authors: Johannes Lederer - Ruhr-University Bochum (Germany)
Michael Vogt - University of Ulm (Germany) [presenting]
Abstract: Much of the theory for the lasso in the high-dimensional linear model $Y = X \beta^* + \varepsilon$ 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 $\beta^*$. We develop a bootstrap-based estimator of the quantiles of the effective noise. The estimator is fully data-driven; that is, it 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 $\beta^*$.
