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 omega. We propose an estimation procedure in two steps: first, we construct an approximation (r) over cap of r, then we use a discrete associated kernel method to estimate nonparametrically the multiplicative correction factor omega = m/(r) over cap. 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. (C) 2012 Elsevier B.V. All rights reserved.