Discrete optimal symmetric kernels for estimating count data distributions

The frequency estimator has long been regarded as the non-parametric reference for count data distributions. Meanwhile, the non-parametric esti-mator using discrete kernels has been developed as one competing alternative to the frequency estimator. Various discrete kernels are now available in the literature, which raises the issue of finding one discrete optimal kernel for non-parametric estimation of count data. To address this issue, we investigated discrete symmetric kernels that minimise the global squared error of non-parametric estimator of count data distributions. Basic asymptotic properties of both discrete optimal symmetric kernels and the corresponding non-parametric estimator were studied, in comparison with other discrete non-parametric kernel estimators. The performance of one discrete optimal symmetric kernel was also illustrated through simulations and applications on real data set.