Exact moments of the product limit estimator

✍ Scribed by Eswar G. Phadia; Peter Yi-Shi Shao

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 105 KB
• Volume: 41
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00164-3

✦ Synopsis

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 speciÿc models. In addition, the ÿrst two exact moments of the two nonparametric estimators of the cumulative hazard function commonly used, are also derived.