Discrete semiparametric regression models with associated kernel and applications

Tristan Senga Kiessé (1) , Michaël Rivoire (2)

1 ONF - Office national des forêts
2 LERFoB - Laboratoire d'Etudes des Ressources Forêt-Bois

This work is concerned with a semiparametric associated kernel estimator for count explanatory variables. The proposed semiparametric estimator is a multiplicative combination between a parametric model and a discrete nonparametric kernel estimator of Nadaraya–Watson type. In this semiparametric approach, the parametric model plays the role of the start function and the nonparametric kernel estimator is a correction factor of the parametric estimate. Some asymptotic properties of the discrete semiparametric kernel regression estimator are pointed out; in particular, we show its asymptotic normality and the order of the optimal bandwidth.The parametric part is illustrated by some nonlinear and generalised linear models; for the nonparametric estimator, we apply the discrete general triangular associated kernel providing bias reduction. The usefulness of the discrete semiparametric kernel regression estimator is shown on three practical examples in comparison with logistic, generalised linear and additive models.

Mots clés: asymptotic normality; bandwidth optimal ordre; discrete regression; parametric regression model

Domaines: Statistiques [math.ST]

Tristan Senga Kiessé, Michaël Rivoire. Discrete semiparametric regression models with associated kernel and applications. Journal of Nonparametric Statistics, 2011, 23 (4), pp.927-941. ⟨10.1080/10485252.2011.583986⟩. ⟨hal-01097970⟩