Multiple Hypotheses Testing For Variable Selection

2011/06/17 by Florian Rohart, Rohart, Florian
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1106.3415

openalex publication_date 2011/06/17 · arxiv created 2012/06/10 · arxiv updated 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Many methods have been developed to estimate the set of relevant variables in a sparse linear model Y= XB+e where the dimension p of B can be much higher than the length n of Y. Here we propose two new methods based on multiple hypotheses testing, either for ordered or non-ordered variables. Our procedures are inspired by the testing procedure proposed by Baraud et al (2003). The new procedures are proved to be powerful under some conditions on the signal and their properties are non asymptotic. They gave better results in estimating the set of relevant variables than both the False Discovery Rate (FDR) and the Lasso, both in the common case (p<n) and in the high-dimensional case (p>n).

Citations

• Model-Consistent Sparse Estimation through the Bootstrap

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