Testing a linear regression model against nonparametric alternatives. (English) Zbl 0785.62049

Summary: As a test statistic for testing goodness-of-fit of a linear regression model, we propose 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 W. Härdle and E. Mammen [Comparing nonparametric versus parametric regression fits. Preprint (1988)]. 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.


62G10 Nonparametric hypothesis testing
62J05 Linear regression; mixed models
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