Testing independence of covariates and errors in nonparametric regression

Consider a nonparametric regression model Y = m(X)+✏, where m is an unknown regression function, Y is a real-valued response variable, X is a real co-variate, and ✏ is the error term. In this article, we extend the usual tests for homoscedasticity by developing consistent tests for independence between X and ✏. Further, we investigate the local power of the proposed tests using Le Cam’s contiguous alternatives. An asymptotic power study under local alternatives along with extensive finite sample simulation study shows the performance of the new tests is competitive with existing ones. Furthermore, the practicality of the new tests is shown using two real data sets.