A class of tests for testing parametric regression against nonparametric alternatives

A class of tests based on adaptive varying kernel regression estimator is proposed for testing parametric regression against nonparametric regression. The tests are integrated squared error functions of adaptive Demir-Toktamiş estimator and conditional expectation of regression function obtained from adaptive varying kernel density estimator. Properties of the proposed tests and their asymptotic distributions are derived. Their performances in terms of empirical power are obtained and are compared with existing tests in the literature. Application of the tests is provided through a real data.