Goodness-of-Fit Test for Monotone Functions

In this article, we develop a test for the null hypothesis that a real-valued function belongs to a given parametric set against the non-parametric alternative that it is monotone, say decreasing. The method is described in a general model that covers the monotone density model, the monotone regression and the right-censoring model with monotone hazard rate. The criterion for testing is an <formula format="inline"><file name="sjos_688_mu1.gif" type="gif" /></formula>-distance between a Grenander-type non-parametric estimator and a parametric estimator computed under the null hypothesis. A normalized version of this distance is shown to have an asymptotic normal distribution under the null, whence a test can be developed. Moreover, a bootstrap procedure is shown to be consistent to calibrate the test. Copyright (c) 2010 Board of the Foundation of the Scandinavian Journal of Statistics.