A Sequential Rejection Testing Method for High-Dimensional Regression with Correlated Variables

Mandozzi Jacopo () and Bühlmann Peter
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Mandozzi Jacopo: Libera AG, Zürich, Switzerland
Bühlmann Peter: Libera AG, Zürich, Switzerland

The International Journal of Biostatistics, 2016, vol. 12, issue 1, 79-95

Abstract: We propose a general, modular method for significance testing of groups (or clusters) of variables in a high-dimensional linear model. In presence of high correlations among the covariables, due to serious problems of identifiability, it is indispensable to focus on detecting groups of variables rather than singletons. We propose an inference method which allows to build in hierarchical structures. It relies on repeated sample splitting and sequential rejection, and we prove that it asymptotically controls the familywise error rate. It can be implemented on any collection of clusters and leads to improved power in comparison to more standard non-sequential rejection methods. We complement the theoretical analysis with empirical results for simulated and real data.

Keywords: familywise error rate; hierarchical clustering; high-dimensional variable selection; inheritance procedure; lasso; linear model; minimal true detection; multiple testing; sample splitting; sequential rejection principle; singleton true detection (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1515/ijb-2015-0008

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