  Much of the theory for the lasso in the 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 $\beta^*$. 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 $\beta^*$.
