Consistent Bootstrap Tests of Parametric Regression Functions.

摘要

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 Cramer-von Mises tests to the regression framework. They are consistent against all alternatives to the null hypothesis, powerful against 1/square-root-of-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 Cramer-von Mises test) have outstanding small sample performance compared to some of the existing tests.