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Biometrika 1996 83(4):763-777; doi:10.1093/biomet/83.4.763
© 1996 by Biometrika Trust
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Corrected confidence intervals after sequential testing with applications to survival analysis

D. S. COAD and M. B. WOODROOFE

School of Mathematical Sciences, University of Sussex Falmer, Brighton BN1 9QH, U.K.
Department of Statistics, University of Michigan Ann Arbor, Michigan 48109-1027, U.S.A.

Corrected confidence intervals are developed for an unknown parameter for data from a sequential experiment. The corrections are obtained from asymptotic expansions for the distribution of the signed root transformation and they have a simple form. The model does not require independent and identically distributed random variables, or smooth stopping boundaries. Inference about the failure rate of an exponential distribution when data are subject to random censoring, censoring by real time, and optional stopping is used to illustrate the main results. The accuracy of the method is confirmed through simulation studies.

Key Words: Approximately pivotal quantity • One-parameter exponential family, Sequential test • Signed root transformation • Stein's identity • Very weak expansion


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