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The asymptotic distribution of the suprema of the standardized empirical processes under the Koziol-Green model

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  • Ghorai, J. K.
  • Schmitter, J.

Abstract

Let denote the m.l.e. of the survival function SX(t) based on the right censored data (Z1,[delta]1),...,(Zn,[delta]n) and the proportional hazards model of random censorship. The asymptotic distribution of certain linear combinations of the supremum of the standardized process is shown to be an extreme value distribution. This limiting distribution is used to construct asymptotically exact confidence bands for the survival function SX over the entire range of the observations. These bands are found to be narrower at both ends of the survival function when compared to the bands obtained by Hollander and Peña. If the proportion of uncensored data, [alpha]n, is greater than , the bands narrow to zero width at both ends of the survival function. The bands are illustrated using simulated as well as real life data sets.

Suggested Citation

  • Ghorai, J. K. & Schmitter, J., 1999. "The asymptotic distribution of the suprema of the standardized empirical processes under the Koziol-Green model," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 303-313, February.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:3:p:303-313
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    References listed on IDEAS

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    1. Cheng, Philip E. & Lin, Gwo Dong, 1987. "Maximum likelihood estimation of a survival function under the koziol-green proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 75-80, January.
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