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Consistent bootstrap tests of parametric regression functions. (English) Zbl 0966.62018
Summary: This paper introduces specification tests of parametric mean-regression models. The null hypothesis of interest is that the parametric regression function is correctly specified. The proposed tests are generalizations of the Kolmogorov-Smirnov and Cramér-von Mises tests to the regression framework. They are consistent against all alternatives to the null hypothesis, powerful against \(1/\sqrt n\) local alternatives, not dependent on any smoothing parameters and simple to compute. A wild-bootstrap procedure is suggested to obtain critical values for the tests and is justified asymptotically. A small-scale Monte Carlo experiment shows that our tests (especially Cramér-von Mises test) have outstanding small sample performance compared to some of the existing tests.

MSC:
62F40 Bootstrap, jackknife and other resampling methods
62G10 Nonparametric hypothesis testing
62P20 Applications of statistics to economics
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