论文标题
通过互补素描对高维线性回归系数的两样本测试
Two-sample testing of high-dimensional linear regression coefficients via complementary sketching
论文作者
论文摘要
我们引入了一种新方法，用于对高维线性回归系数进行两样本测试，而不假设这些系数是可以估算的。该过程首先将协变量的矩阵和响应向量沿指示进行了互补，这些矩阵在坐标子集中是互补的，我们称之为“补充素描”的过程。当两个回归系数之间的差异分别稀疏和密集时，所得的投影协变量和响应汇总为两种测试统计量，在高斯设计下，这些统计量基本上具有最佳的渐近功率。仿真确认我们的方法在广泛的设置中的表现良好，并且对大型单细胞RNA测序数据集的应用程序显示了其在现实世界中的实用性。
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.
