Nonparametric testing for a monotone hazard function via normalized spacings

Abstract

We study the problem of testing whether a hazard function is monotonic or not. The proposed test statistics, a global test and four localized tests, are all based on normalized spacings. The global test is in fact just the test statistic [Proschan, F. and Pyke, R. (1967). Tests for monotone failure rate. Fifth Berkeley Symposium, 3, 293–313], introduced for testing a constant hazard function versus a nondecreasing nonconstant hazard function. This global test is powerful for detecting global departures of the null hypothesis, but lacks power when there are local departures from the null hypothesis. By localizing the global test, we obtain tests that respond to this drawback. We also show how the testing procedures can be used when dealing with Type II censored data. We evaluate the performance of the test statistics via simulation studies and illustrate them on some data sets.

E-mail: [email protected]

Keywords:

• Monotone hazard function
• Order statistics
• Spacings
• Type II censoring

Acknowledgements

This research was supported by ‘Projet d’Actions de Recherche Concertées’, No. 98/03-217 of the Belgian government, by IAP research network no. P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) and by the Natural Sciences and Engineering Research Council of Canada. The second author would like to thank the Institute of Pure and Applied Mathematics and the Institute of Statistics of the Université Catholique de Louvain, for the financial support and their hospitality. Both authors thank Michael Akritas and an anonymous referee for their careful reading of the paper.

Notes

E-mail: [email protected]