Testing monotonicity of regression functions - an empirical process approach

We propose several new tests for monotonicity of regression functions based on different empirical processes of residuals. The residuals are obtained from recently developed simple kernel based estimators for increasing regression functions based on increasing rearrangements of unconstrained nonparametric estimators. The test statistics are estimated distance measures between the regression function and its increasing rearrangement. We discuss the asymptotic distributions, consistency, and small sample performances of the tests. AMS Classification: 62G10, 62G08, 62G3