An approach to nonparametric smoothing techniques for regressions with discrete data

This paper proposes nonparametric regression estimation techniques for small samples in situations where the dependent variable involves count data. Often the form of a kernel will not matter asymptotically. However, in small samples the kernel structure may play a more important role in approximating the small sample distribution especially for discrete random variables. In particular for count data we introduce a Poisson kernel regression estimator and a binomial kernel regression estimator. These new regression methods are applied to coal mine wildcat strike data. We use cross validation to evaluate out-of-sample performance.