Kernel Selection in Nonparametric Regression

Hélène Halconruy (1, 2) , Nicolas Marie (3, 1)

1 ESME - ESME - École spéciale de mécanique et d'électricité
2 IMT - Institut Mines-Télécom [Paris]
3 MODAL'X - Modélisation aléatoire de Paris X

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.

Domaines: Statistiques [math.ST]

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