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Testing procedures for assessing a parametric regression model with circularresponse and $\mathbb{R}^d$-valued covariate are proposed and analyzed in thiswork both for independent and for spatially correlated data. The teststatistics are based on a circular distance comparing a (non-smoothed orsmoothed) parametric circular estimator and a nonparametric one. Properlydesigned bootstrap procedures for calibrating the tests in practice are alsopresented. Finite sample performance of the tests in different scenarios withindependent and spatially correlated samples, is analyzed by simulations.

Goodness-of-fit tests for parametric regression models with circular response