Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks

Details Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks

2005-09-04

arxiv.org/abs/math/0509084v2

Scandinavian Journal of Statistics 2008, Vol. 35, No. 1, 83-103

Mathematics

Statistics Theory

27 pages, 4 figures

Scientific paper

10.1111/j.1467-9469.2007.00568.x

This paper considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this problem. We use this formula and the mark specific cumulative hazard function of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This result leads to necessary and sufficient conditions for consistency of the MLE which imply that the MLE is inconsistent in general. We show that the inconsistency can be repaired by discretizing the marks. Our theoretical results are supported by simulations.

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