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Drift estimation on non compact support for diffusion models

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  • Comte, Fabienne
  • Genon-Catalot, Valentine

Abstract

We study non parametric drift estimation for an ergodic diffusion process from discrete observations. The drift is estimated on a set A using an approximate regression equation by a least squares contrast, minimized over finite dimensional subspaces of L2(A,dx). The novelty is that the set A is non compact and the diffusion coefficient unbounded. Risk bounds of a L2-risk are provided where new variance terms are exhibited. A data-driven selection procedure is proposed where the dimension of the projection space is chosen within a random set contrary to usual selection procedures.

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  • Comte, Fabienne & Genon-Catalot, Valentine, 2021. "Drift estimation on non compact support for diffusion models," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 174-207.
    • Handle: RePEc:eee:spapps:v:134:y:2021:i:c:p:174-207
    DOI: 10.1016/j.spa.2021.01.001
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    References listed on IDEAS

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    1. Gwennaëlle Mabon, 2017. "Adaptive Deconvolution on the Non-negative Real Line," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 707-740, September.
    2. F. Comte & V. Genon-Catalot, 2020. "Regression function estimation on non compact support in an heteroscesdastic model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 93-128, January.
    3. Hoffmann, Marc, 1999. "Adaptive estimation in diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 135-163, January.
    4. Fabienne Comte & Charles-A. Cuenod & Marianna Pensky & Yves Rozenholc, 2017. "Laplace deconvolution on the basis of time domain data and its application to dynamic contrast-enhanced imaging," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 69-94, January.
    5. 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.
    6. Strauch, Claudia, 2015. "Sharp adaptive drift estimation for ergodic diffusions: The multivariate case," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2562-2602.
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    Cited by:

    1. Comte, Fabienne & Marie, Nicolas, 2023. "Nonparametric drift estimation from diffusions with correlated Brownian motions," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    2. Nicolas Marie, 2023. "Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models," Finance and Stochastics, Springer, vol. 27(1), pages 97-126, January.

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