Isotonic L2-projection test for local monotonicity of a hazard

We introduce a test statistic for testing the null hypothesis that the sampling distribution has a strictly increasing hazard rate on a specified interval [ a , b ] . It is based on a comparison of the empirical distribution function with a shape-constrained estimate, using the restriction that the hazard is increasing. Its asymptotic (normal) distribution was recently derived in Groeneboom and Jongbloed (submitted for publication). We discuss a bootstrap method for computing the critical values and compare the test, thus obtained, with other recently proposed methods in a simulation study. Moreover, we prove that the bootstrap method works asymptotically. In proving that the (smooth and isotonic) bootstrap method works, we derive some results that seem to be of independent interest.