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Sub-exponentiality in Statistical Exponential Models

Author

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  • Barbara Trivellato

    (Politecnico di Torino)

Abstract

Improvements in the study of nonparametric maximal exponential models built on Orlicz spaces are proposed. By exploiting the notion of sub-exponential random variable, we give theoretical results which provide a clearer insight into the structure of these models. The explicit constants we obtain when changing the law of Orlicz spaces centered at connected densities allow us to derive uniform bounds with respect to a reference density.

Suggested Citation

  • Barbara Trivellato, 2024. "Sub-exponentiality in Statistical Exponential Models," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2076-2096, September.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:3:d:10.1007_s10959-023-01281-6
    DOI: 10.1007/s10959-023-01281-6
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    References listed on IDEAS

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    1. Alberto Cena & Giovanni Pistone, 2007. "Exponential statistical manifold," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(1), pages 27-56, March.
    2. M. Grasselli, 2010. "Dual connections in nonparametric classical information geometry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 873-896, October.
    3. Siri, Paola & Trivellato, Barbara, 2021. "Robust concentration inequalities in maximal exponential models," Statistics & Probability Letters, Elsevier, vol. 170(C).
    Full references (including those not matched with items on IDEAS)

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