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Biometrika Advance Access first published online on February 7, 2007
This version published online on February 14, 2007
Biometrika, doi:10.1093/biomet/asm002
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Copyright © Biometrika Trust

Interval censoring: identifiability and the constant-sum property

Ramon Oller, Guadalupe Gómez and Luz M. Calle

Departament d'Economia, Matemàtica i Informàtica de la Universitat de Vic, Sagrada Familia 7, 08500 Vic., Spain
Departament d'Estadística i Investigació Operativa de la Universitat Politècnica de Catalunya, Jordi Girona 1-3, Edifici C5, Campus Nord, 08034 Barcelona, Spain
Departament de Biologica de Sistemes, Universitat de Vic, Sagrada Família 7, 08500 Vic. Barcelona, Spain

ramon.oller{at}uvic.cat

lupe.gomez{at}upc.edu

malu.calle{at}uvic.cat

Received for publication 1 April 2005. Revision received 1 May 2006.
  Abstract

The constant-sum property given in Oller et al. (2004) for censoring models justifies the use of a simplified likelihood to obtain the nonparametric maximum likelihood estimator of the lifetime distribution. In this paper we study the relevance of the constant-sum property in the identifiability of the lifetime distribution. We show that the lifetime distribution is not identifiable outside the class of constant-sum models. We also show that the lifetime probabilities assigned to the observable intervals are identifiable inside the class of constant-sum models. We illustrate all these notions with several examples.

Key Words: constant-sum condition • EM-algorithm • Turnbull interval

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