Appropriate kernel regression on a count explanatory variable and applications
Résumé
We propose an appropriate nonparametric regression on a single count regressor using a recent discrete kernel approach. We adapt the Nadaraya-Watson estimator to this discrete kernel for smoothing the regression function on count data. Some properties are studied; in particular, the bandwidth selection is investigated through the crossvalidation method. The proposed regression, in addition to being simple, easy to implement and effective, outperforms the competing usual regressions for small and moderate sample sizes. Using simulations and two examples from real life, the importance and the performance of discrete kernels are pointed out and compared with the optimal continuous kernel.
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