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Exact moments of the product limit estimator

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  • Phadia, Eswar G.
  • Shao, Peter Yi-Shi

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.

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  • Phadia, Eswar G. & Shao, Peter Yi-Shi, 1999. "Exact moments of the product limit estimator," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 277-286, February.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:3:p:277-286
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    References listed on IDEAS

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    1. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
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    1. Chen, Zhiqiang & Phadia, Eswar, 2006. "An optimal completion of the product limit estimator," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 913-919, May.
    2. Jiantian Wang, 2008. "Small-sample studies on right censored data with discrete failure times," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 427-440, June.

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