Isotonic L_2-projection test for local monotonicity of a hazard
  We introduce a new test statistic for testing the null hypothesis that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. It is based on a comparison of the empirical distribution function with an isotonic estimate, using the restriction that the hazard is increasing, and measures the excursions of the empirical distribution above the isotonic estimate, due to local non-monotonicity. It is proved in the companion paper Groeneboom and Jongbloed (2011a) that the test statistic is asymptotically normal if the hazard is strictly increasing on the interval [0,a] and certain regularity conditions are satisfied. We discuss a bootstrap method for computing the critical values and compare the test, thus obtained, with other proposals in a simulation study. 
Piet Groeneboom and Geurt Jongbloed
math.ST stat.TH