Linear Functional Testing with General Loadings in Sparse Regression: Separation Rates and Computational Barriers
稀疏回归中一般载荷的线性泛函检验:分离率与计算障碍
We study the problem of testing $H_0: ξ^\topβ=t_0$ in high-dimensional sparse linear regression with Gaussian random design and unknown design covariance. The loading vector $ξ$ is arbitrary, and the exact sparsity level $k$ is unknown but bounded by a known value $k_u$. Tests are required to control Type I error uniformly over the $k_u$-sparse null, while power is evaluated against $k$-sparse alternatives. We construct a computationally efficient mixed test that gives an…