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On statistical inference for random closed sets in compact subsets of ℝd

Part of: Inference from stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

J. Ferrándiz  and
F. Montes
J. Ferrándiz*
Affiliation:
Universitat de València
F. Montes*
Affiliation:
Universitat de València
*
* Postal address: Departament d'Estadística i I.O., Universitat de València, Dr. Moliner 50, E-46100 Burjassot, Spain.
* Postal address: Departament d'Estadística i I.O., Universitat de València, Dr. Moliner 50, E-46100 Burjassot, Spain.
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Abstract

Quite often in the statistical analysis of medical and biological problems, data are images corresponding to entire objects that include smaller objects within them. In these cases, we need models of random closed sets (RACS) confined to compact subsets of the plane. There is no room for stationarity hypotheses and the increase of statistical information comes from independent replicates of the same phenomena rather than increasing our sample window. We investigate practical methods of modelling RACS by means of circumscribed balls, leading to a natural definition of location, size and shape. We discuss the possibilities of using these random variables in order to define statistical spaces of RACS that will allow us to use maximum likelihood methods.

Keywords

RANDOM COMPACT SETSMAXIMUM LIKELIHOOD ESTIMATION

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 2 , June 1995 , pp. 344 - 349
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This work has been partially supported by the Generalitat Valenciana, Grant GV-1081/93.

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain, on 21–24 September 1993.

References

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