136
Views
18
CrossRef citations to date
0
Altmetric
Miscellany

Nonparametric testing for a monotone hazard function via normalized spacings

&
Pages 463-477 | Received 22 Jan 2003, Accepted 30 Jul 2003, Published online: 31 Jan 2007

References

References

  • Ahmad , IA . (1975) . A nonparametric test for the monotonicity of a failure rate function . Commun. Stat. A-Theor. , A4 : 967 – 974 .
  • Bain LJ (1978) Statistical Analysis of Reliability and Life-testing Models: Theory and Methods, M. Dekker New York
  • Barlow , RE and Doksum , K . (1972) . Isotonic tests for convex orderings . Proceedings of the Sixth Berkeley Symposium , 1 : 293 – 323 .
  • Barlow RE Proschan F (1965) Mathematical Theory of Reliability, The SIAM series in Applied Mathematics, John Wiley New York
  • Barlow , RE and Proschan , F . (1969) . A note on tests for monotone failure rate based on incomplete data . Ann. Math. Stat. , 40 : 595 – 600 .
  • Bickel , PJ . (1969) . Tests for monotone failure rate II . Ann. Math. Stat. , 40 : 1250 – 1260 .
  • Bickel , PJ and Doksum , KA . (1969) . Tests for monotone failure rate based on normalized spacings . Ann. Math. Stat. , 40 : 1216 – 1235 .
  • Dümbgen , L . (2002) . Application of local rank tests to nonparametric regression . J. Nonparametr. Stat. , 14 : 511 – 537 .
  • Epstein , B and Sobel , M . (1953) . Life testing . J. Am. Stat. Assoc. , 48 : 486 – 502 .
  • Gail , MH and Gastwirth , JL . (1978a) . A scale-free goodness-of-fit test for the exponential distribution based on the Lorentz curve . J. Am. Stat. Assoc. , 73 : 787 – 793 .
  • Gail , MH and Gastwirth , JL . (1978b) . A scale-free goodness-of-fit test for the exponential distribution based on the Gini statistic . J. Roy. Stat. Soc. B , 40 : 350 – 357 .
  • Gerlach , B . (1987) . Testing exponentiality against increasing failure rate with randomly censored data . Statistics , 18 : 275 – 268 .
  • Gijbels , I , Hall , P , Jones , MC and Koch , I . (2000) . Tests for monotonicity of a regression mean with guaranteed level . Biometrika , 87 : 663 – 673 .
  • Grenander , U . (1956) . On the theory of mortality measurement, Part II . Skand. Akt. , 39 : 125 – 153 .
  • Gupta , AK . (1952) . Estimation of the mean and standard deviation of a normal population from a censored sample . Biometrika , 39 : 260 – 273 .
  • Hall , P and Heckman , N . (2000) . Testing for monotonicity of a regression mean by calibrating for linear functions . Ann. Stat. , 28 : 20 – 39 .
  • Hall , P , Huang , L-S , Gifford , J and Gijbels , I . (2001) . Nonparametric estimation of hazard rate under the constraint of monotonicity . J. Comput. Graph. Stat. , 10 : 592 – 614 .
  • Hall , P and Presnell , B . (1999) . Intentionally biased bootstrap methods . J. Roy. Stat. Soc. B , 61 : 259 – 277 .
  • Hall P Van Keilegom I (2002) Testing for monotone increasing hazard rate manuscript
  • Huang , J and Wellner , J . (1995) . Estimation of a monotone density or monotone hazard under random censoring . Scand. J. Stat. , 22 : 3 – 33 .
  • Klefsjö , B . (1983) . Some tests against aging based on the total time on test transform . Commun. Stat. A-Theor. , A12 : 907 – 927 .
  • Kumazawa , Y . (1992) . Tests for increasing failure rate with randomly censored data . Statistics , 23 : 17 – 25 .
  • Lawless JF (1982) Statistical Models and Methods for Lifetime Data, Wiley New York
  • Lieblein , J and Zelen , M . (1956) . Statistical investigation of fatigue life of deep groove ball bearings . J. Res. Nat. Bur. Stand. , 57 : 273 – 316 .
  • Mann , HB . (1945) . Nonparametric tests against trend . Econometrica , 13 : 245 – 259 .
  • Marshall , AW and Proschan , F . (1965) . Maximum likelihood estimation for distributions with monotone failure rate . Ann. Math. Stat. , 36 : 69 – 77 .
  • Mukerjee , H and Wang , J-L . (1993) . Nonparametric maximum likelihood estimation of an increasing hazard rate for uncertain cause-of-death data . Scand. J. Stat. , 20 : 17 – 33 .
  • Myktyn , S and Santner , T . (1981) . Maximum likelihood estimation of the survival function based on censored data under hazard rate assumptions . Communications in Statistics–Theory & Methods , A10 : 1369 – 1387 .
  • Nelson , WB . (1969) . Hazard plotting for incomplete failure data . J. Qual. Technol. , 1 : 27 – 52 .
  • Padgett , WJ and Wei , LJ . (1980) . Maximum likelihood estimation of a distribution function with increasing failure rate based on censored observations . Biometrika , 67 : 470 – 474 .
  • Proschan , F and Pyke , R . (1967) . Tests for monotone failure rate . Fifth Berkeley Symposium , 3 : 293 – 313 .
  • Robertson T Wright FT Dykstra RL (1988) Order Restricted Statistical Inference, Wiley New York
  • Tiku , ML . (1967) . Estimating the mean and standard deviation from a censored normal sample . Biometrika , 54 : 155 – 165 .
  • Tsai , WY . (1988) . Estimation of the survival function with increasing failure rate based on left truncated and right censored date . Biometrika , 75 : 319 – 324 .
  • Wang , J-L . (1986) . Asymptotically minimax estimators for distributions with increasing failure rate . Ann. Stat. , 14 : 1113 – 1131 .
  • Watson , GS and Leadbetter , MR . (1964a) . Hazard Analysis I . Biometrika , 51 : 175 – 184 .
  • Watson , GS and Leadbetter , MR . (1964b) . Hazard Analysis II . Sankhyã A , 26 : 101 – 116 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.