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L2 differentiability of generalized linear models

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  • Pupashenko, Daria
  • Ruckdeschel, Peter
  • Kohl, Matthias

Abstract

We derive conditions for L2 differentiability of generalized linear models with error distributions not necessarily belonging to exponential families, covering both cases of stochastic and deterministic regressors. These conditions induce smoothness and integrability conditions for corresponding GLM-based time series models.

Suggested Citation

  • Pupashenko, Daria & Ruckdeschel, Peter & Kohl, Matthias, 2015. "L2 differentiability of generalized linear models," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 155-164.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:155-164
    DOI: 10.1016/j.spl.2014.11.020
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    1. Dahen, Hela & Dionne, Georges, 2010. "Scaling models for the severity and frequency of external operational loss data," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1484-1496, July.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    3. Marc Hallin & Yvik Swan & Thomas Verdebout & David Veredas, 2011. "Rank-based testing in linear models with stable errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 305-320.
    4. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
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    Cited by:

    1. Tino Werner, 2022. "Asymptotic linear expansion of regularized M-estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 167-194, February.
    2. Laudagé, Christian & Desmettre, Sascha & Wenzel, Jörg, 2019. "Severity modeling of extreme insurance claims for tariffication," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 77-92.
    3. Anders Bredahl Kock & David Preinerstorfer, 2019. "Power in High‐Dimensional Testing Problems," Econometrica, Econometric Society, vol. 87(3), pages 1055-1069, May.

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