A consistent test of functional form via nonparametric estimation techniques. (English) Zbl 0865.62030

Summary: This paper presents a consistent test of functional form of nonlinear regression models. The test combines the methodology of the conditional moments test and nonparametric estimation techniques. Using degenerate and nondegenerate \(U\)-statistics theories, the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct, while diverging to infinity at a rate arbitrarily close to \(n\), the sample size, if the parametric model is misspecified. Therefore, the test is consistent against all deviations from the parametric model. The test is robust to heteroskedasticity. A version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate \(1/\sqrt n\). A simulation study reveals that the test has good finite-sample properties.


62G07 Density estimation
62J02 General nonlinear regression
62E20 Asymptotic distribution theory in statistics
62P20 Applications of statistics to economics
62F03 Parametric hypothesis testing
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