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The Two‐interval Line‐segment Problem

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  • Mark J. Van Der Laan

Abstract

In this paper we define and study the non‐parametric maximum likelihood estimator (NPMLE) in the one‐dimensional line‐segment problem, where we observe line‐segments on the real line through an interval with a gap which is smaller than the two remaining intervals. We define the self‐consistency equations for the NPMLE and provide a quick algorithm for solving them. We prove supremum norm weak convergence to a Gaussian process and efficiency of the NPMLE. The problem has a geological application in the study of the lifespan of species

Suggested Citation

  • Mark J. Van Der Laan, 1998. "The Two‐interval Line‐segment Problem," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 163-186, March.
    • Handle: RePEc:bla:scjsta:v:25:y:1998:i:1:p:163-186
    DOI: 10.1111/1467-9469.00096
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