Two-sample testing of high-dimensional linear regression coefficients via complementary sketching
Two-sample testing of high-dimensional linear regression coefficients via complementary sketching
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DOI：
10.1214/22-aos2216
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发表时间：
2020-11
期刊：
影响因子：
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通讯作者：
Fengnan Gao;Tengyao Wang
中科院分区：
文献类型：
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作者：
Fengnan Gao;Tengyao Wang
本文介绍了一种新的高维线性回归系数的双样本检验方法，而不需要假设这些系数是单独可估计的。该过程的工作原理是首先将协变量矩阵和响应向量沿沿着方向投影，这些方向在坐标的子集中符号互补，我们称之为“互补草图”。由此产生的投影协变量和响应汇总，形成两个测试统计量，这是具有基本上最佳的渐近功率下的高斯设计时，两个回归系数之间的差异分别是稀疏和密集。模拟证实，我们的方法在广泛的设置类执行良好。
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.