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A simple consistent bootstrap test for a parametric regression function. (English) Zbl 0943.62031
Summary: A simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form. It is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result. We also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative. Monte Carlo simulations suggest that the bootstrap test performs well based on ‘wild bootstrap’ critical values.

MSC:
62F40 Bootstrap, jackknife and other resampling methods
62F03 Parametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
62J02 General nonlinear regression
65C05 Monte Carlo methods
Software:
KernSmooth
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