Estimates for the score function under random censoring (Q1090026)

Assuming that \(X_ 1,...X_ n\) is a random sample of lifetimes from a distribution with density f subject to random right-censoring the author proposes and studies the strong consistency of an estimator of the score function f'(x)/f(x). The estimator which is based on random spacings of order statistics extends to the censored data case the idea of the histogram density estimator of \textit{J. Van Ryzin}, Comun. Statist. 2, 493-506 (1973; Zbl 0283.62040) as well as the estimation of the derivative of a density in \textit{B. K. Kim} and \textit{J. Van Ryzin}, Commun. Stat., Theory Methods A 9, 697-709 (1980; Zbl 0437.62043).