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Biometrika 1994 81(3):618-623; doi:10.1093/biomet/81.3.618
© 1994 by Biometrika Trust
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MISCELLANEA

Maximum likelihood for interval censored data: Consistency and computation

ROBERT GENTLEMAN1 and CHARLES J. GEYER2

1 Department of Statistics, University of Auckland Private Bag 92019, Auckland, New Zealand
2 School of Statistics, University of Minnesota 206 Church Street S.E., Minneapolis, Minnesota, 55455, U.S.A.

Received for publication 1 January 1991. Revision received 1 October 1993.
  Abstract

Standard convex optimization techniques are applied to the analysis of interval censored data. These methods provide easily verifiable conditions for the self-consistent estimator proposed by Turnbull (1976) to be a maximum likelihood estimator and for checking whether the maximum likelihood estimate is unique. A sufficient condition is given for the almost sure convergence of the maximum likelihood estimator to the true underlying distribution function.

Key Words: Convergence • Self-consistency algorithm • Uniqueness


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