Gijbels, Irène
[UCL]
Heckman, N
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.
- Ahmad Ibrahim A., A nonparametric test for the monotonicity of a failure rate function, 10.1080/03610927508827305
- Bain LJ, Statistical Analysis of Reliability and Life-testing Models: Theory and Methods, M. Dekker (1978)
- Barlow RE, Proceedings of the Sixth Berkeley Symposium, 1, 293 (1972)
- Barlow RE, Mathematical Theory of Reliability, The SIAM series in Applied Mathematics, John Wiley (1965)
- Barlow R. E., Proschan F., A Note on Tests for Monotone Failure Rate Based on Incomplete Data, 10.1214/aoms/1177697727
- Bickel P. J., Tests for Monotone Failure Rate II, 10.1214/aoms/1177697500
- Bickel Peter J., Doksum Kjell A., Tests for Monotone Failure Rate Based on Normalized Spacings, 10.1214/aoms/1177697498
- Dümbgen Lutz, Application of local rank tests to nonparametric regression, 10.1080/10485250213903
- Epstein Benjamin, Sobel Milton, Life Testing, 10.1080/01621459.1953.10483488
- Gail MH, J. Am. Stat. Assoc., 73, 787 (1978)
- Gail MH, J. Roy. Stat. Soc. B, 40, 350 (1978)
- Gerlach B., Testing exponentiality against increasing failure rate with randomly censored data, 10.1080/02331888708802019
- Gijbels I, Tests for monotonicity of a regression mean with guaranteed level, 10.1093/biomet/87.3.663
- Grenander U, Skand. Akt., 39, 125 (1956)
- GUPTA A. K., ESTIMATION OF THE MEAN AND STANDARD DEVIATION OF A NORMAL POPULATION FROM A CENSORED SAMPLE, 10.1093/biomet/39.3-4.260
- Heckman Nancy E., Hall Peter, linear functions, 10.1214/aos/1016120363
- Hall Peter, Huang Li-Shan, Gifford James A, Gijbels Irene, Nonparametric Estimation of Hazard Rate Under the Constraint of Monotonicity, 10.1198/106186001317115135
- Hall P, J. Roy. Stat. Soc. B, 61, 259 (1999)
- Hall P Van Keilegom I (2002) Testing for monotone increasing hazard rate manuscript
- Huang J, Scand. J. Stat., 22, 3 (1995)
- Klefsjö Bengt, Some tests against aging based on the total time on test transform, 10.1080/03610928308828505
- Kumazawa Yoshiki, Tests for increasing failure rate with randomly censored data, 10.1080/02331889208802349
- Lawless JF, Statistical Models and Methods for Lifetime Data, Wiley (1982)
- Lieblein J., Zelen M., Statistical investigation of the fatigue life of deep-groove ball bearings, 10.6028/jres.057.033
- Mann Henry B., Nonparametric Tests Against Trend, 10.2307/1907187
- Marshall Albert W., Proschan Frank, Maximum Likelihood Estimation for Distributions with Monotone Failure Rate, 10.1214/aoms/1177700271
- Mukerjee H, Scand. J. Stat., 20, 17 (1993)
- Mykytyn Stephen W., Santner Thomas J., Maximum likelihood estimation of the survival function based on censored data under hazard rate assumptions, 10.1080/03610928108828120
- Nelson WB, J. Qual. Technol., 1, 27 (1969)
- PADGETT W. J., WEI L. J., Maximum likelihood estimation of a distribution function with increasing failure rate based on censored observations, 10.1093/biomet/67.2.470
- Proschan F, Fifth Berkeley Symposium, 3, 293 (1967)
- Robertson T, Order Restricted Statistical Inference, Wiley (1988)
- TIKU M. L., Estimating the mean and standard deviation from a censored normal sample, 10.1093/biomet/54.1-2.155
- TSAI WEI-YANN, Estimation of the survival function with increasing failure rate based on left truncated and right censored data, 10.1093/biomet/75.2.319
- Wang Jane-Ling, Asymptotically Minimax Estimators for Distributions with Increasing Failure Rate, 10.1214/aos/1176350053
- WATSON G. S., LEADBETTER M. R., Hazard analysis. I, 10.1093/biomet/51.1-2.175
- Watson GS, Sankhyã A, 26, 101 (1964)
Bibliographic reference |
Gijbels, Irène ; Heckman, N. Nonparametric testing for a monotone hazard function via normalized spacings.International Conference on Recent Advances and Trends in NonParametric Statistics (IRAKLION(Greece), Jul 15-19, 2002). In: Journal of Nonparametric Statistics, Vol. 16, no. 3-4, p. 463-477 (2004) |
Permanent URL |
http://hdl.handle.net/2078.1/61284 |