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The Two‐interval Line‐segment Problem
Author(s) -
Van Der Laan Mark J.
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00096
Subject(s) - mathematics , infimum and supremum , real line , estimator , consistency (knowledge bases) , uniform norm , interval (graph theory) , line (geometry) , line segment , parametric statistics , gaussian , combinatorics , mathematical analysis , statistics , discrete mathematics , geometry , quantum mechanics , physics
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