Title: Nonparametric regression estimation with a circular response and a functional covariable
Authors: Andrea Meilan-Vila - Carlos III University of Madrid (Spain) [presenting]
Rosa Crujeiras - University of Santiago de Compostela (Spain)
Mario Francisco-Fernandez - Universidade da Coruna (Spain)
Abstract: The analysis of a variable of interest that depends on other variables (s) is a typical issue appearing in many practical problems. Regression analysis provides the statistical tools to address this type of problem. This topic has been deeply studied, especially when the variables are of the Euclidean type. However, there are situations where the data present certain kind of complexities, for example, the involved variables are of circular or functional type, and the classical regression procedures designed for Euclidean data may not be appropriate. In these scenarios, these techniques would have to be conveniently modified to provide useful results. A nonparametric estimator of the circular regression function for models with a circular response and a functional covariate are introduced. Specifically, a Nadaraya-- Watson type estimator is proposed and studied. The asymptotic bias and variance of the estimator, as well as, its asymptotic distribution are calculated. Some guidelines for its practical implementation are provided, checking its sample performance through simulations. Finally, the behavior of the estimator is also illustrated with a real data set.