标题： 留一法交叉验证对套索（lasso）是一致的风险估计器 显示英文标题

标题： Leave-one-out cross-validation is risk consistent for lasso

摘要： 套索（lasso）方法在统计学和信号处理文献中无处不在，因此成为大量理论和应用研究的目标。 尽管这些研究大多关注套索所具有的理想特性——预测风险一致性、符号一致性、正确模型选择——但所有研究都假设平滑参数是以最优方式选择的。 然而，在实际操作中这是不可能做到的。 相反，数据分析师必须两次使用数据：一次用于选择平滑参数，另一次用于估计模型。 但迄今为止，只有启发式的方法可以为此程序提供依据。 为此，我们给出了首个关于套索风险一致性的确定性答案，当平滑参数通过交叉验证选择时。 我们证明了在设计矩阵的一些限制条件下，即使采用经验选择的平滑参数，套索估计器仍然具有风险一致性。 显示英文摘要

摘要： The lasso procedure is ubiquitous in the statistical and signal processing literature, and as such, is the target of substantial theoretical and applied research. While much of this research focuses on the desirable properties that lasso possesses---predictive risk consistency, sign consistency, correct model selection---all of it has assumes that the tuning parameter is chosen in an oracle fashion. Yet, this is impossible in practice. Instead, data analysts must use the data twice, once to choose the tuning parameter and again to estimate the model. But only heuristics have ever justified such a procedure. To this end, we give the first definitive answer about the risk consistency of lasso when the smoothing parameter is chosen via cross-validation. We show that under some restrictions on the design matrix, the lasso estimator is still risk consistent with an empirically chosen tuning parameter.