On semiparametric regression for count explanatory variables

This work deals with a semiparametric estimation of a count regression function m that can be represented as a product of an unknown discrete parametric function r   and an unknown discrete “smooth” function ωω. We propose an estimation procedure in two steps: first, we construct an approximation r^ of r  , then we use a discrete associated kernel method to estimate nonparametrically the multiplicative correction factor ω=m/r^. The asymptotic and small-sample properties of the proposed estimator are investigated. Its comparison with the classical Nadaraya–Watson type count regression estimator shows that an improvement in terms of bias is achieved.