Asymptotic Theory of the Sparse Group LASSO

2016/11/18 by Benjamin Poignard, Poignard, Benjamin
Engineering · Mathematics · Medicine · #FOS: Mathematics #Liver Disease Diagnosis and Treatment #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1611.06034

openalex publication_date 2016/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proposes a general framework for penalized convex empirical criteria and a new version of the Sparse-Group LASSO (SGL, Simon and al., 2013), called the adaptive SGL, where both penalties of the SGL are weighted by preliminary random coefficients. We explore extensively its asymptotic properties and prove that this estimator satisfies the so-called oracle property (Fan and Li, 2001), that is the sparsity based estimator recovers the true underlying sparse model and is asymptotically normally distributed. Then we study its asymptotic properties in a double-asymptotic framework, where the number of parameters diverges with the sample size. We show by simulations that the adaptive SGL outperforms other oracle-like methods in terms of estimation precision and variable selection.

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