On semiparametric regression for count explanatory variables

Belkacem Abdous (1) , Célestin C. Kokonendji (2) , Tristan Senga Kiessé (3)

1 DMPS - Département de médecine sociale et préventive
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 ONF - Office national des forêts

We study the problem of semiparametric estimation of a multivariate count regression function m : Nd -> R that can be represented as a product of an unknown discrete parametric function r and an unknown discrete smooth function w. For the construction of such estimators, we first find an approximation result br for the parametric part r, and then estimate the nonparametric multiplicative correction factor w = m/br by a discrete associated-kernel method. Comparisons are therefore carried out with the nonparametric count regression estimator of Nadaraya-Watson type. We point out that the new semiparametric count regression estimator can reduce the bias with respect to purely nonparametric count regression estimator, without affecting the variance.

Mots clés: Asymptotic bias and variance; Discrete associated kernel; Discrete finite difference; Multiplicative correction factor; Nonparametric regression; Nadaraya-Watson estimator; Logistic regression

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

Belkacem Abdous, Célestin C. Kokonendji, Tristan Senga Kiessé. On semiparametric regression for count explanatory variables. Journal of Statistical Planning and Inference, 2012, 142 (6), pp.1537-1548. ⟨10.1016/j.jspi.2012.01.006⟩. ⟨hal-00952385⟩