## 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.

### MSC:

 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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### References:

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