Linear Functional Testing with General Loadings in Sparse Regression: Separation Rates and Computational Barriers

Jie Xie, Dongming Huang

We study the problem of testing $H_0:\hat{I}{¾}^{\top }{\hat{I}}^2=t_0$ in high-dimensional sparse linear regression with Gaussian random design and unknown design covariance. The loading vector $\hat{I}¾$…