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Tests for a Family of Survival Models Based on Extremes

  • Martin Crowder
Part of the Statistics for Industry and Technology book series (SIT)

Abstract

Some tests based on extreme order statistics are proposed for a certain family of survival models. The parametric hypotheses to be tested specify values on the boundary of the parameter space. In such cases likelihood-based tests often do not have the usual regularity properties, and may not even provide useful test statistics, whereas extremes-based tests can be effective. Some previous work is extended here to a more general setting. This entails a wider range of possibilities and also brings out some aspects not present under more restricted models.

Keywords and phrases

Asymptotic theory boundary hypotheses extreme values local power function survival model test consistency 

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References

  1. 1.
    Cheng, R.C.H. and Stephens, M.A. (1989). A goodness-of-fit test using Moran’s statistic with estimated parameters. Biometrika, 76, 385–392.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Cheng, R.C.H. and Traylor, L. (1994). Non-regular maximum likelihood problems (with discussion). J. R. Statist. Soc. B, 57, 3–44.MathSciNetGoogle Scholar
  3. 3.
    Crowder, M.J. (1990). On some nonregular tests for a modified Weibull model. Biometrika, 77, 499–506.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Crowder, M.J. (1996). Some tests based on extreme values for a parametric survival model. J. Roy. Statist. Soc. B, 58, 417–424.MathSciNetzbMATHGoogle Scholar
  5. 5.
    Crowder, M.J. (1997). A multivariate model for repeated failure time measurements. Scand. J. Statist., 25, 53–67.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kimber, A.C. (1990). Exploratory data analysis for possibly censored data from skewed distributions. Appl. Statist., 39, 21–30.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    NAG (1988). Library Manual Mark 13. Oxford: Numerical Algorithms Group.Google Scholar
  8. 8.
    Smith, R.L. (1989). A survey of nonregular problems. Proc. 47th Session, Int. Statist. Inst. Paris.Google Scholar
  9. 9.
    Watson, A.S. and Smith, R.L. (1985). An examination of statistical theories for fibrous materials in the light of experimental data. J. Mater. Sci., 20, 3260–3270.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Martin Crowder
    • 1
  1. 1.Surrey UniversityGuildfordEngland

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