Semiparametric multiple kernel estimators and model diagnostics for count regression functions

Lamia Djerroud (1) , Tristan Senga Kiessé (2) , Smail Adjabi (1)

1 Unité de recherche LaMOS = Research unit LaMOS - Unité de recherche Laboratoire de Modélisation et Optimisation des Systèmes [Université de Béjaïa]
2 SAS - Sol Agro et hydrosystème Spatialisation

This study concerns semiparametric approaches to estimate discrete multivariate count regression functions. The semiparametric approaches investigated consist of combining discrete multivariate nonparametric kernel and parametric estimations such that (i) a prior knowledge of the conditional distribution of model response may be incorporated and (ii) the bias of the traditional nonparametric kernel regression estimator of Nadaraya-Watson may be reduced. We are precisely interested in combination of the two estimations approaches with some asymptotic properties of the resulting estima-tors. Asymptotic normality results were showed for nonparametric correction terms of parametric start function of the estimators. The performance of discrete semiparametric multivariate kernel estimators studied is illustrated using simulations and real count data. In addition, diagnostic checks are performed to test the adequacy of the parametric start model to the true discrete regression model. Finally, using discrete semiparametric multivariate kernel estimators provides a bias reduction when the parametric multivari-ate regression model used as start regression function belongs to a neighbourhood of the true regression model.

Mots clés: Semiparametric count regression; Discrete multivariate kernel; Cross-validation; Model diagnostics

Domaines: Mathématiques [math]; Statistiques [math.ST]

Lamia Djerroud, Tristan Senga Kiessé, Smail Adjabi. Semiparametric multiple kernel estimators and model diagnostics for count regression functions. Communications in Statistics - Theory and Methods, 2019, pp.1-27. ⟨10.1080/03610926.2019.1568488⟩. ⟨hal-02058897⟩