Two-sample testing of high-dimensional linear regression coefficients via complementary sketching
提出一种不要求系数可单独估计的高维线性回归系数双样本检验方法，通过互补投影构造检验统计量，在稀疏和密集差异下均有最优渐近功效，模拟和单细胞RNA测序数据验证了其有效性。
We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and response vectors along directions that are complementary in sign in a subset of the coordinates, a process which we call “complementary sketching.” The resulting projected covariates and responses are aggregated to form two test statistics, which are shown to have essentially optimal asymptotic power under a Gaussian design when the difference between the two regression coefficients is sparse and dense respectively. Simulations confirm that our methods perform well in a broad class of settings and an application to a large single-cell RNA sequencing dataset demonstrates its utility in the real world.