Nonparametric estimation from incomplete observations. (English) Zbl 0089.14801

Kaplan, E. L.; Meier, Paul

J. Am. Stat. Assoc. 53, 457-481 (1958).

Let \(P(t)\) be the probability that an item from a given population will have lifetime exceeding \(t\). For a sample of size \(N\) let the observed times either to death or to other loss be \(t_1\leq t_2\leq t_3\leq \cdots\leq t_n\). The maximum likelihood estimate of \(P(t)\) is then \[ \widehat{P(t)}=\prod_r \frac{(N-r)}{(N-r+1)} \] where \(r\) ranges over those integers for which \(t_r\leq t\) and \(t_r\) is a time to death. The mean and variance of \(\widehat{P(t)}\) are computed. Comparisons of this estimate are made with reduced sample estimates and actuarial estimates.

Reviewer: D. R. Whitney

MSC:

62G05	Nonparametric estimation
62G08	Nonparametric regression and quantile regression

Keywords:

statistics