Testing Constancy for Isotonic Regressions

In this paper, we propose a bootstrap method for testing the constancy of an isotonic regression. The technique we develop is completely non-parametric and enlarges the appli-cability of the classical chi-bar-squared tests, which require normality assumptions. We prove that our procedure is asymptotically correct and consistent. Moreover, by means of simulations we show that it behaves suitably in practice, and similarly to the chi-bar-squared tests under normality. Finally, we illustrate the method with the study of a real case that is well known in the related literature.