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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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    3. 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.
    4. Okhrin Ostap & Okhrin Yarema & Schmid Wolfgang, 2013. "Properties of hierarchical Archimedean copulas," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 21-54, March.
    5. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. Fermanian, Jean-David & Lopez, Olivier, 2018. "Single-index copulas," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 27-55.
    8. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2013. "On the structure and estimation of hierarchical Archimedean copulas," Journal of Econometrics, Elsevier, vol. 173(2), pages 189-204.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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