The survival curve under monotone density constraints with applications to two-dimensional line segment processes

Abstract

Several situations involving survival data are examined, in which the nonparametric maximum likelihood estimator is not the Kaplan-Meier estimator. Cases covered are inclusion of initial observations in field studies, estimation of the length distribution from convex window sampling of line segment processes in two dimensions, and estimation of a survival curve with monotone density. The first two cases are nonstandard because survival and censoring are not independent, and thus form simple tractable variable-sum models (Williams & Lagakos, 1977).