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Regression function estimation on non compact support in an heteroscesdastic model

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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.

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Authors and Affiliations

  1. Laboratoire MAP5 UMR CNRS 8145, Université Paris Descartes, Paris, France

    F. Comte & V. Genon-Catalot

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  1. F. Comte
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  2. V. Genon-Catalot
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Correspondence to F. Comte.

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Comte, F., Genon-Catalot, V. Regression function estimation on non compact support in an heteroscesdastic model. Metrika 83, 93–128 (2020). https://doi.org/10.1007/s00184-019-00727-4

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  • DOI: https://doi.org/10.1007/s00184-019-00727-4

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