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The finite sample properties of Sparse M-estimators with Pseudo-Observations

Author

Listed:
  • Benjamin Poignard

    (Osaka University, Graduate School of Engineering Science.)

  • Jean-David Fermanian

    (CREST; ENSAE.)

Abstract

We provide finite sample properties of general regularized statistical criteria in the presence of pseudo-observations. Under the restricted strong convexity assump-tion of the unpenalized loss function and regularity conditions on the penalty, we derive non-asymptotic error bounds on the regularized M-estimator that hold with high probability. This penalized framework with pseudo-observations is then ap-plied 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, 2019. "The finite sample properties of Sparse M-estimators with Pseudo-Observations," Working Papers 2019-01, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2019-01
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    References listed on IDEAS

    as
    1. Hofert, Marius & Pham, David, 2013. "Densities of nested Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 37-52.
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    6. Okhrin, Ostap & Ristig, Alexander & Sheen, Jeffrey R. & Trück, Stefan, 2015. "Conditional systemic risk with penalized copula," SFB 649 Discussion Papers 2015-038, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
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    8. Segers, Johan & Uyttendaele, Nathan, 2014. "Nonparametric estimation of the tree structure of a nested Archimedean copula," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 190-204.
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