PROPERTIES FOR CIRCULAR NONPARAMETRIC REGRESSIONS BY VON MIESE AND WRAPPED CAUCHY KERNELS

We discuss the asymptotic properties with respect to nonparametric regression for circular data. We reveal theoretical properties for circular nonparametric regression by applying von Mises (VM) and wrapped Cauchy (WC) kernels. We derive the asymptotic normalities and the convergence rate of the weighted conditional mean integrated squared errors regarding VM and WC kernels. The numerical experiment shows that WC kernel outperforms VM kernel in the small samples, and the theoretical properties are supported in the large samples.