A General Framework for Estimation and Inference From Clusters of Features
针对预测变量有预设分组的问题，提出基于响应变量构建组原型并用似然比检验的方法，相比经典F检验或t检验有更高统计功效，并利用选择性推断保证检验有效性。
Applied statistical problems often come with prespecified groupings to predictors. It is natural to test for the presence of simultaneous group-wide signal for groups in isolation, or for multiple groups together. Current tests for the presence of such signals include the classical F-test or a t-test on unsupervised group prototypes (either group centroids or first principal components). In this article, we propose test statistics that aim for power improvements over these classical approaches. In particular, we first create group prototypes, with reference to the response, and then test with likelihood ratio statistics incorporating only these prototypes. We propose a model, called the “prototype model,” which naturally models this two-step procedure. Furthermore, we introduce an inferential schema detailing the unique considerations for different combinations of prototype formation and univariate/multivariate testing models. The prototype model also suggests new applications to estimation and prediction. Prototype formation often relies on variable selection, which invalidates classical Gaussian test theory. We use recent advances in selective inference to account for selection in the prototyping step and retain test validity. Simulation experiments suggest that our testing procedure enjoys more power than do classical approaches. Supplementary materials for this article are available online.