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Kernel Selection in Nonparametric Regression

Abstract : In the regression model $Y = b(X) +\sigma(X)\varepsilon$, where $X$ has a density $f$, this paper deals with an oracle inequality for an estimator of $bf$, involving a kernel in the sense of Lerasle et al. (2016), selected via the PCO method. In addition to the bandwidth selection for kernel-based estimators already studied in Lacour, Massart and Rivoirard (2017) and Comte and Marie (2020), the dimension selection for anisotropic projection estimators of $f$ and $bf$ is covered.
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https://hal.archives-ouvertes.fr/hal-02867190
Contributor : Nicolas Marie Connect in order to contact the contributor
Submitted on : Saturday, March 20, 2021 - 9:34:12 PM
Last modification on : Wednesday, November 3, 2021 - 6:31:34 AM

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  • HAL Id : hal-02867190, version 2

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Hélène Halconruy, Nicolas Marie. Kernel Selection in Nonparametric Regression. Mathematical Methods of Statistics, Allerton Press, Springer (link), 2020, 29 (1), pp.31-55. ⟨hal-02867190v2⟩

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