A Conditional Kolmogorov Test

This paper introduces a conditional Kolmogorov test of model specification for parametric models with covariates (regressors). The test is an extension of the Kolmogorov test of goodness-of-fit for distribution functions. The test is shown to have power against 1/root{n}-local alternatives and all fixed alternatives to the null hypothesis. A parametric bootstrap procedure is used to obtain critical values for the test.