A consistent test for the functional form of a regression based on a difference of variance estimators

In this paper we study the problem of testing the functional farm of a give n regression model. A consistent test is proposed which is based on the dif ference of the least squares variance estimator in the assumed regression m odel and a nonparametric variance estimator. The corresponding test statist ic can be shown to be asymptotically normal under the null hypothesis and u nder fixed alternatives with different rates of convergence corresponding t o both cases. This provides a simple asymptotic test, where the asymptotic results can also be used for the calculation of the type II error of the pr ocedure at any particular point of the alternative and for the construction of tests for precise hypotheses. Finally, the finite sample performance of the new test is investigated in a detailed simulation study, which also co ntains a comparison with the commonly used tests.