A high-dimensional M-estimator framework for bi-level variable selection

Bin Luo () and Xiaoli Gao
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Bin Luo: Duke University
Xiaoli Gao: The University of North Carolina at Greensboro

Annals of the Institute of Statistical Mathematics, 2022, vol. 74, issue 3, No 8, 559-579

Abstract: Abstract In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and sparsity can appear either at the group level or within certain groups. In such cases, an ideal model should be able to encourage the bi-level variable selection consistently. Bi-level variable selection has become even more challenging when data have heavy-tailed distribution or outliers exist in random errors and covariates. In this paper, we study a framework of high-dimensional M-estimation for bi-level variable selection. This framework encourages bi-level sparsity through a computationally efficient two-stage procedure. In theory, we provide sufficient conditions under which our two-stage penalized M-estimator possesses simultaneous local estimation consistency and the bi-level variable selection consistency if certain non-convex penalty functions are used at the group level. Both our simulation studies and real data analysis demonstrate satisfactory finite sample performance of the proposed estimators under different irregular settings.

Keywords: Bi-level variable selection; Estimation consistency; High dimensionality; M-estimation; Non-convexity (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10463-021-00809-z

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