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On a projection least squares estimator for jump diffusion processes

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  • Hélène Halconruy

    (Léonard de Vinci Pôle universitaire, Research Center)

  • Nicolas Marie

    (Université Paris Nanterre)

Abstract

This paper deals with a projection least squares estimator of the drift function of a jump diffusion process X computed from multiple independent copies of X observed on [0, T]. Risk bounds are established on this estimator and on an associated adaptive estimator. Finally, some numerical experiments are provided.

Suggested Citation

  • Hélène Halconruy & Nicolas Marie, 2024. "On a projection least squares estimator for jump diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(2), pages 209-234, April.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:2:d:10.1007_s10463-023-00881-7
    DOI: 10.1007/s10463-023-00881-7
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    References listed on IDEAS

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    1. Denis Belomestny & Fabienne Comte & Valentine Genon-Catalot, 2019. "Sobolev-Hermite versus Sobolev nonparametric density estimation on $${\mathbb {R}}$$ R," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 29-62, February.
    2. Maud Delattre & Valentine Genon-Catalot & Adeline Samson, 2013. "Maximum Likelihood Estimation for Stochastic Differential Equations with Random Effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 322-343, June.
    3. Picchini, Umberto & Ditlevsen, Susanne, 2011. "Practical estimation of high dimensional stochastic differential mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1426-1444, March.
    4. F. Comte & V. Genon-Catalot, 2020. "Regression function estimation as a partly inverse problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1023-1054, August.
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