2015/02/11 by Jacopo Mandozzi, Peter Bühlmann, Mandozzi, Jacopo +1
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1502.03300
openalex publication_date 2015/02/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We propose a general, modular method for significance testing of groups (or\nclusters) of variables in a high-dimensional linear model. In presence of high\ncorrelations among the covariables, due to serious problems of identifiability,\nit is indispensable to focus on detecting groups of variables rather than\nsingletons. We propose an inference method which allows to build in\nhierarchical structures. It relies on repeated sample splitting and sequential\nrejection, and we prove that it asymptotically controls the familywise error\nrate. It can be implemented on any collection of clusters and leads to improved\npower in comparison to more standard non-sequential rejection methods. We\ncomplete the theoretical analysis with empirical results for simulated and real\ndata.\n