Testing a linear regression model against nonparametric alternatives

As a test statistic for testing goodness-of-fit of a linear regression model, the paper proposes a ratio of quadratic forms measuring the distance between parametric and nonparametric fits, relative to the estimated error variance. The test statistic is a modification of the statistic suggested by Härdle and Mammen. The asymptotic distribution under the hypothesis is established. The finite sample behaviour of the test is investigated in a Monte Carlo study, and is illustrated for two applications.