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A limit theorem for statistics of spatial data

Published online by Cambridge University Press:  01 July 2016

Adrian Baddeley
Adrian Baddeley*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, U.K.
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Abstract

A large class of statistics of planar and spatial data is closely connected with empirical distributions, which estimate ‘ergodic’ distributions of stationary random sets. The main result is a functional limit theorem concerning the deviation of the empirical distribution from the ‘true’ one. Examples in mathematical morphology are given.

Keywords

EMPIRICAL DISTRIBUTIONSMATHEMATICAL MORPHOLOGYRANDOM SETSRANDOM FIELDSFUNCTIONAL CENTRAL LIMIT THEOREM
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 2 , June 1980 , pp. 447 - 461
Copyright
Copyright © Applied Probability Trust 1980 

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