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Inference for stationary random fields given Poisson samples

Published online by Cambridge University Press:  01 July 2016

Alan F. Karr
Alan F. Karr*
Affiliation:
The Johns Hopkins University
*
∗Postal address: Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA.
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Abstract

Given a d-dimensional random field and a Poisson process independent of it, suppose that it is possible to observe only the location of each point of the Poisson process and the value of the random field at that (randomly located) point. Non-parametric estimators of the mean and covariance function of the random field—based on observation over compact sets of single realizations of the Poisson samples—are constructed. Under fairly mild conditions these estimators are consistent (in various senses) as the set of observation becomes unbounded in a suitable manner. The state estimation problem of minimum mean-squared error reconstruction of unobserved values of the random field is also examined.

Keywords

NON-PARAMETRIC COVARIANCE APPROXIMATIONSTATE ESTIMATION
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 2 , June 1986 , pp. 406 - 422
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research support by the Air Force Office of Scientific Research, grant number AFOSR 82-0029B. The United States Government is authorized to reproduce and distribute reprints for governmental purposes.

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