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

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Listed:
  • 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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    References listed on IDEAS

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    1. Hofert, Marius & Pham, David, 2013. "Densities of nested Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 37-52.
    2. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    3. 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.
    4. 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.
    5. Ostap Okhrin & Alexander Ristig & Jeffrey Sheen & Stefan Trück, 2015. "Conditional Systemic Risk with Penalized Copula," SFB 649 Discussion Papers SFB649DP2015-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. 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.
    7. 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.
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