论文标题
估计拉索的有效噪音
Estimating the Lasso's Effective Noise
论文作者
论文摘要
线性模型中拉索的大部分理论$ y =xβ^* + \ varepsilon $ hinges the Wentity $ 2 \ | x^\ top \ varepsilon \ | _ {\ infty} / n $，我们称之为拉索的有效噪声。除其他外，有效噪声在套索的有限样本边界，套索调整参数的校准以及参数矢量$β^*$的推断中起着重要作用。在本文中，我们开发了一个基于自举的有效噪声分位数的估计器。估计器是完全数据驱动的，也就不需要任何其他调整参数。我们为估算器配备有限样本的保证，并将其应用于套索的调整参数校准，并对参数矢量$β^*$的高度推断。
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 $β^*$.
