Testing Many Zero Restrictions in a High Dimensional Linear Regression Setting
提出一种在高维线性回归模型中检验多个参数是否为零的方法，通过逐个估计低维模型中的关键参数，无需稀疏性假设，计算速度快于去偏Lasso，并提供了参数自助法计算p值。
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with k ≫ n regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension regression models with nuisance terms. The parsimoniously parameterized models identify whether the original parameter of interest is or is not zero. Estimating fixed low dimension sub-parameters ensures greater estimator accuracy, it does not require a sparsity assumption nor therefore a regularized estimator, it is computationally fast compared to, for example, de-biased Lasso, and using only the largest in a sequence of weighted estimators reduces test statistic complexity and therefore estimation error. We provide a parametric wild bootstrap for p-value computation, and prove the test is consistent and has nontrivial n/{ ln (n)Mn} -local-to-null power where Mn is the l∞ covariate fourth moment.