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Laslett's line segment problem

Published online by Cambridge University Press:  01 July 2016

Richard D. Gill
Richard D. Gill*
Affiliation:
Utrecht University
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Extract

Consider A Stationary Line Segment Process In The Plane, Observed Through A Window W. Line Segments Which Cross The Boundary Of The Window Are Only Partially Observed. One Might Say That The Observed Lengths Of The Line Segments Are Then Censored. However, Classical Methods From The Theory Of Censored Survival Data (Kaplan-Meier Estimator) Can Be Seen To Be Inappropriate.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 332
Copyright
Copyright © Applied Probability Trust 1996 

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References

Gill, R. D. (1994) Lectures on survival analysis. In Lectures on Probability Theory: Ecole d'Eté de Probabilités de Saint Flour XXII-1992. (Springer Lecture Notes in Mathematics 1581) ed. Bernard, P. pp 115–241.Google Scholar
van der Laan, M. J. (1995) Efficiency of the NPMLE in the line-segment problem. Scand. J. Statist. to appear.Google Scholar
Laslett, G. M. (1982) The survival curve under monotone density constraints with application to two-dimensional line-segment processes. Biometrika 69, 153–160.Google Scholar
Wijers, B. J. (1995a) Consistent non-parametric estimation for a one-dimensional line segment process observed in an interval. Scand. J. Statist. 22, 335–360.Google Scholar
Wijers, B. J. (1995b) Nonparametric estimation for a Windowed Line Segment Process. , University of Utrecht.Google Scholar