Comparing nonparametric versus parametric regression fits. (English) Zbl 0795.62036

The authors consider the problem to test the parametric model \(\{m_ \theta\); \(\theta\in\Theta\}\) against the nonparametric alternative that only assumes \(m(\cdot)\) is ‘smooth’. They propose to use as a test statistics the integrated squared deviation of the parametric and nonparametric curve estimate. They show that the standard way of bootstrapping this statistics fails, however, wild bootstrap works. The validity of the asymptotic results is checked in a Monte Carlo experiment and on the fitting Engel curves in the mean expediture curve of a certain food.
Reviewer: M.Huškova (Praha)


62G07 Density estimation
62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
62F99 Parametric inference
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