Sharp Threshold Detection Based on Sup-Norm Error Rates in High-Dimensional Models
提出了阈值化缩放Lasso估计量，利用上确界范数误差界实现高维阈值回归中零与非零系数的精细区分，并通过模拟和债务与GDP增长关系的实证研究展示了其变量选择优势。
We propose a new estimator, the thresholded scaled Lasso, in high-dimensional threshold regressions. First, we establish an upper bound on the ℓ∞ estimation error of the scaled Lasso estimator of Lee, Seo, and Shin. This is a nontrivial task as the literature on high-dimensional models has focused almost exclusively on ℓ1 and ℓ2 estimation errors. We show that this sup-norm bound can be used to distinguish between zero and nonzero coefficients at a much finer scale than would have been possible using classical oracle inequalities. Thus, our sup-norm bound is tailored to consistent variable selection via thresholding. Our simulations show that thresholding the scaled Lasso yields substantial improvements in terms of variable selection. Finally, we use our estimator to shed further empirical light on the long-running debate on the relationship between the level of debt (public and private) and GDP growth. Supplementary materials for this article are available online.