Goodness-of-fit tests for parametric regression models

Several new tests are proposed for examining the adequacy of a family of pa rametric models against large nonparametric alternatives. These tests forma lly check if the bias vector of residuals from parametric fts is negligible by using the adaptive Neyman test and other methods. The testing procedure s formalize the traditional model diagnostic tools based on residual plots. We examine the rates of contiguous alternatives that can be detected consi stently by the adaptive Neyman test. Applications of the procedures to the partially linear models are thoroughly discussed. Our simulation studies sh ow that the new testing procedures are indeed powerful and omnibus. The pow er of the proposed tests is comparable to the F-test statistic even in the situations where the F test is known to be suitable and can be far more pow erful than the F-test statistic in other situations. An application to test ing linear models versus additive models is also discussed.