An equality test across nonparametric regressions

We propose a procedure for testing the equality of several nonparametric multivariate regressions. We allow the regressors’ designs and the number of observations to differ across subsamples. The division into subsamples is defined through a variable C which can be either fixed or random. For a random C, our procedure is a general test of significance for qualitative variables in a nonparametric regression. For a fixed C, our procedure provides a ‘nonparametric analysis of covariance’, which is valid for cross-section or panel data. In both cases, the test is a one-sided normal test and is consistent against all alternatives.