2015/11/24 by Stephen Reid, Reid, Stephen, Jonathan Taylor +3
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1511.07839
openalex publication_date 2015/11/24 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Applied statistical problems often come with pre-specified groupings to\npredictors. It is natural to test for the presence of simultaneous group-wide\nsignal for groups in isolation, or for multiple groups together. Classical\ntests for the presence of such signals rely either on tests for the omission of\nthe entire block of variables (the classical F-test) or on the creation of an\nunsupervised prototype for the group (either a group centroid or first\nprincipal component) and subsequent t-tests on these prototypes.\n In this paper, we propose test statistics that aim for power improvements\nover these classical approaches. In particular, we first create group\nprototypes, with reference to the response, hopefully improving on the\nunsupervised prototypes, and then testing with likelihood ratio statistics\nincorporating only these prototypes. We propose a (potentially) novel model,\ncalled the "prototype model", which naturally models the two-step\nprototype-then-test procedure. Furthermore, we introduce an inferential schema\ndetailing the unique considerations for different combinations of prototype\nformation and univariate/multivariate testing models. The prototype model also\nsuggests new applications to estimation and prediction.\n Prototype formation often relies on variable selection, which invalidates\nclassical Gaussian test theory. We use recent advances in selective inference\nto account for selection in the prototyping step and retain test validity.\nSimulation experiments suggest that our testing procedure enjoys more power\nthan do classical approaches.\n