A simple consistent bootstrap test for a parametric regression function

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 bootstrapʹ critical values.