Isotonic L_2-projection test for local monotonicity of a hazard

TL;DR

This paper proposes a new statistical test for detecting local non-monotonicity in hazard functions, based on isotonic regression and empirical distribution comparisons, with theoretical and simulation validation.

Contribution

It introduces a novel test statistic for local hazard monotonicity, including asymptotic properties and a bootstrap method for critical value computation.

Findings

Test statistic is asymptotically normal under strict increasing hazard.

Bootstrap method effectively computes critical values.

Simulation study compares the new test with existing methods.

Abstract

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.