Exact moments of the product limit estimator

In this article we derive the exact kth moment of the product limit estimator without any assumption on the underlying survival distribution model. An approximate formula is also derived which is more amenable to estimation. Under the assumption of the proportional hazard model these results special...

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Bibliographic Details
Published in:Statistics & probability letters 1999-02, Vol.41 (3), p.277-286
Main Authors: Phadia, Eswar G., Shao, Peter Yi-Shi
Format: Article
Language:English
Subjects:
Censored data
Distribution theory
Exact sciences and technology
Mathematics
Moments
Nonparametric estimation
Nonparametric estimation Moments Product limit estimator Censored data
Probability and statistics
Product limit estimator
Sciences and techniques of general use
Statistics
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Summary:In this article we derive the exact kth moment of the product limit estimator without any assumption on the underlying survival distribution model. An approximate formula is also derived which is more amenable to estimation. Under the assumption of the proportional hazard model these results specialize to those obtained by Chen et al. (1982, J. Am. Statist. Assoc. 77, 141–144). Biases and comparative performances of commonly used asymptotic variance formulas with the exact and approximate formulas are discussed numerically for some specific models. In addition, the first two exact moments of the two nonparametric estimators of the cumulative hazard function commonly used, are also derived.
ISSN:0167-7152
1879-2103
DOI:10.1016/S0167-7152(98)00164-3