The Two-Interval Line-Segment Problem
In this paper, the NPMLE in the one-dimensional line segment problem is defined and studied, where line segments on the real line through two non-overlapping intervals are observed. The self-consistency equations for the NPMLE are defined and a quick algorithm for solving them is provided. Supnorm weak convergence to a Gaussian process and efficiency of the NPMLE is proved. The problem has a strong geological application in the study of the lifespan of species.
van der Laan, Mark J., "The Two-Interval Line-Segment Problem" (September 1995). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 54.