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

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  • Benjamin Poignard

    (Osaka University
    RIKEN Center for Advanced Intelligence Project (AIP)
    CREST-LFA)

  • Jean-David Fermanian

    (Ensae-Crest)

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.

Suggested Citation

  • Benjamin Poignard & Jean-David Fermanian, 2022. "The finite sample properties of sparse M-estimators with pseudo-observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 1-31, February.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:1:d:10.1007_s10463-021-00785-4
    DOI: 10.1007/s10463-021-00785-4
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