Improving kernel-based nonparametric regression for circular-linear data

We discuss kernel-based nonparametric regression where a predictor has support on a circle and a responder has support on a real line. Nonparametric regression is used in analyzing circular-linear data because of its flexibility. However, nonparametric regression is generally less accurate than an appropriate parametric regression for a population model. Considering that statisticians need more accurate nonparametric regression models, we investigate the performance of sine series local polynomial regression while selecting the most suitable kernel class. The asymptotic result shows that higher-order estimators reduce conditional bias; however, they do not improve conditional variance. We show that higher-order estimators improve the convergence rate of the weighted conditional mean integrated square error. We also prove the asymptotic normality of the estimator. We conduct a numerical experiment to examine a small sample of characteristics of the estimator in scenarios wherein the error term is homoscedastic or heterogeneous. The result shows that choosing a higher degree improves performance under the finite sample in homoscedastic or heterogeneous scenarios. In particular, in some scenarios where the regression function is wiggly, higher-order estimators perform significantly better than local constant and linear estimators.