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Title: Testing parametric regression models with circular response Authors:  Andrea Meilan-Vila - Carlos III University of Madrid (Spain) [presenting]
Mario Francisco-Fernandez - Universidade da Coruna (Spain)
Rosa Crujeiras - University of Santiago de Compostela (Spain)
Abstract: Testing procedures for assessing a parametric regression model with a circular response and a $\mathbb{R}^d$-valued covariate are proposed and analyzed. The considered test statistics are based on a comparison between a (non-smoothed or smoothed) parametric fit under the null hypothesis and a nonparametric estimator of the circular regression function. More specifically, two different test statistics are designed. In the first one, a parametric estimator of the regression function under the null hypothesis is directly used. In contrast, in the second one, a smooth version of this estimator is employed. The null hypothesis that the regression function belongs to a certain parametric family is rejected if a suitable circular distance between both fits exceeds a certain threshold. Different bootstrap procedures to calibrate the tests in practice are presented. Finite sample performance of the tests in several scenarios is analyzed by simulations. An illustration with a real dataset is also provided.