The finite sample properties of sparse M-estimators with pseudo-observations

Benjamin Poignard () and Jean-David Fermanian ()
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Benjamin Poignard: Osaka University
Jean-David Fermanian: Ensae-Crest

Annals of the Institute of Statistical Mathematics, 2022, vol. 74, issue 1, No 1, 31 pages

Abstract: Abstract We provide finite sample properties of general regularized statistical criteria in the presence of pseudo-observations. Under the restricted strong convexity assumption of the unpenalized loss function and regularity conditions on the penalty, we derive non-asymptotic error bounds on the regularized M-estimator. This penalized framework with pseudo-observations is then applied to the M-estimation of some usual copula-based models. These theoretical results are supported by an empirical study.

Keywords: Copulas; Non-convex regularizer; Pseudo-observations; Statistical consistency (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10463-021-00785-4

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