Exact moments of the product limit estimator

Eswar G. Phadia and Peter Yi-Shi Shao

Statistics & Probability Letters, 1999, vol. 41, issue 3, 277-286

Abstract: 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.

Keywords: Nonparametric; estimation; Moments; Product; limit; estimator; Censored; data (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (2)

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