Multiplicative Bias Corrected Nonparametric Smoothers

Nicolas Hengartner (1) , Eric Matzner-Løber (2, 3) , Laurent Rouvière (2, 4) , Thomas Burr (1)

1 LANL - Theorical Division
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 UR2 - Université de Rennes 2
4 CREST - Centre de Recherche en Économie et Statistique

The paper presents a multiplicative bias reduction estimator for nonparametric regression. The approach consists to apply a multiplicative bias correction to an oversmooth pilot estimator. In Burr et al. [2010], this method has been tested to estimate energy spectra. For such data set, it was observed that the method allows to decrease bias with negligible increase in variance. In this paper, we study the asymptotic properties of the resulting estimate and prove that this estimate has zero asymptotic bias and the same asymptotic variance as the local linear estimate. Simulations show that our asymptotic results are available for modest sample sizes.

Mots clés: Nonparametric regression; bias reduction; local linear estimate

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Nicolas Hengartner, Eric Matzner-Løber, Laurent Rouvière, Thomas Burr. Multiplicative Bias Corrected Nonparametric Smoothers. Nonparametric statistics, Springer proceedings in Mathematics and Statistics, 3rd ISNPS, Avignon, 2016., 2018, ⟨10.1007/978-3-319-96941-1_3⟩. ⟨hal-00408696v3⟩