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Handling with Spatial Censored Observations in Statistics of Boolean Models of Random Sets
Author(s) -
Molchanov Ilya S.,
Molchanov Ilya S.
Publication year - 1992
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710340510
Subject(s) - mathematics , boolean model , set (abstract data type) , discrete mathematics , random variable , statistics , combinatorics , computer science , programming language
Abstract Let A be a Boolean model. The existing methods of statistical estimation of its parameters are extended to the case when the observation of A is spoiled by a certain hindrance. It means that we observe another set A' instead of A. E.g. the set A′ may take the form A or A where is a stationary random set (assumed to be hindrance) with a known distribution. This construction generalizes the methods of statistics of censored observations to random sets. A brief description of statistical methods for Boolean models is included. All methods rely on the notion of the empirical capacity functional and use Glivenko‐Cantelli theorem for random closed sets.