Thresholding tests based on affine LASSO to achieve non-asymptotic nominal level and high power under sparse and dense alternatives in high dimension
提出基于仿射LASSO的阈值检验方法，生成新的枢轴统计量，在高维稀疏或密集备择假设下具有高功效，并通过蒙特卡洛计算临界值实现精确水平。
Thresholding estimators such as the existing square-root and LAD LASSO, and the new affine and GLM LASSO with new link functions, have the ability to set coefficients to zero. They will yield new pivotal statistics which enjoy high power under sparse or dense alternative hypotheses. Under a general formalism, thresholding tests not only recover existing tests such as Rao score test and Fisher nonparametric sign test, but also unveil new tests, for the global/omnibus hypothesis in high dimension in particular. Although pivotal, the new statistics do not have a known distribution, so the critical value of the test is calculated by straightforward Monte Carlo, which yields exact level and high power as illustrated on simulated data.