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Regression function estimation on non compact support in an heteroscesdastic model

Author

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  • F. Comte

    (Université Paris Descartes)

  • V. Genon-Catalot

    (Université Paris Descartes)

Abstract

We study the problem of nonparametric regression function estimation on non necessarily compact support in a heteroscedastic model with non necessarily bounded variance. A collection of least squares projection estimators on m-dimensional functional linear spaces is built. We prove new risk bounds for the estimator with fixed m and propose a new selection procedure relying on inverse problems methods leading to an adaptive estimator. Contrary to more standard cases, the data-driven dimension is chosen within a random set and the penalty is random. Examples and numerical simulations results show that the procedure is easy to implement and provides satisfactory estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:1:d:10.1007_s00184-019-00727-4
    DOI: 10.1007/s00184-019-00727-4
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    References listed on IDEAS

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    1. Jin, Sainan & Su, Liangjun & Xiao, Zhijie, 2015. "Adaptive Nonparametric Regression With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1153-1191, December.
    2. Comte, F. & Rozenholc, Y., 2002. "Adaptive estimation of mean and volatility functions in (auto-)regressive models," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 111-145, January.
    3. 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.
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    Cited by:

    1. 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.
    2. Florian Dussap, 2023. "Nonparametric multiple regression by projection on non-compactly supported bases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 731-771, October.
    3. 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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