High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local heritability. Group inference in regression models can be measured with respect to a weighted quadratic functional of the regression sub-vector corresponding to the group. Asymptotically unbiased estimators of these weighted quadratic functionals are constructed and a novel procedure using these estimators for inference is proposed. We derive its asymptotic Gaussian distribution which enables the construction of asymptotically valid confidence intervals and tests which perform well in terms of length or power. The proposed test is computationally efficient even for a large group, statistically valid for any group size and achieving good power performance for testing large groups with many small regression coefficients. We apply the methodology to several interesting statistical problems and demonstrate its strength and usefulness on simulated and real data.
翻译:高维群集推断是分析复杂数据集的统计方法的一个基本部分,包括等级测试、互动测试、检测不同处理效应和当地遗传性的推论。回归模型中的群推论可以测量回归子矢量与该组相对应的回归子矢量的加权二次函数的加权二次函数。这些加权二次函数的随机公正的估测器已经构建,并提出了一个使用这些推论的估测器的新程序。我们从中得出其无症状的高斯分布,从而能够构建在长度或功率方面运行良好的无症状有效置信间隔和测试。拟议的测试在计算上是有效的,即使对于一个大组来说也是有效的,对任何组体大小都具有统计上有效,并且能够以许多小回归系数测试大组群体,从而取得良好的功率性。我们将这一方法应用于几个有趣的统计问题,并展示其在模拟和真实数据上的力量和有用性。