Nonparametric multiple regression estimation for circular response

Abstract

Nonparametric estimators of a regression function with circular response and $${\mathbb {R}}^d$$ -valued predictor are considered in this work. Local polynomial estimators are proposed and studied. Expressions for the asymptotic conditional bias and variance of these estimators are derived, and some guidelines to select asymptotically optimal local bandwidth matrices are also provided. The finite sample behavior of the proposed estimators is assessed through simulations, and their performance is also illustrated with a real data set.