Regression function estimation on non compact support in an heteroscesdastic model

F. Comte () and V. Genon-Catalot ()
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F. Comte: Université Paris Descartes
V. Genon-Catalot: Université Paris Descartes

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 1, No 5, 93-128

Abstract: 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.

Keywords: Heteroscedatic regression model; Least squares estimation; Model selection; Projection estimator (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00184-019-00727-4

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