Resampling-Based Multisplit Inference for High-Dimensional Regression

arXiv (Cornell University)

Abstract

We propose a novel resampling-based method to construct an asymptotically exact test for any subset of hypotheses on coefficients in high-dimensional linear regression. It can be embedded into any multiple testing procedure to make confidence statements on relevant predictor variables. The method constructs permutation test statistics for any individual hypothesis by means of repeated splits of the data and a variable selection technique; then it defines a test for any subset by suitably aggregating its variables' test statistics. The resulting procedure is extremely flexible, as it allows different selection techniques and several combining functions. We present it in two ways: an exact method and an approximate one, that requires less memory usage and shorter computation time, and can be scaled up to higher dimensions. We illustrate the performance of the method with simulations and the analysis of real gene expression data.

Authors 3

1. Anna Vesely

   University of Padua

   Affiliation as printed

   Department of Developmental Psychology and Socialization , University of Padova

2. Jelle J. Goeman Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences , Leiden University Medical Center

3. Livio Finos

   University of Padua

   Affiliation as printed

   Department of Developmental Psychology and Socialization , University of Padova