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Asymptotic distribution of a discrete transform of an arbitrarily sampled homogeneous random field

Published online by Cambridge University Press:  01 July 2016

David A. Swick
David A. Swick*
Affiliation:
U. S. Naval Research Laboratory
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Abstract

Multidimensional sampling of real data, e.g., in space and time, often requires observations at non-uniformly spaced intervals. A discrete transform of a multidimensional stationary stochastic process transforms a multivariate problem into an asymptotically univariate one if the spacing is uniform in at least one dimension. For both uniform and non-uniform sampling and a model of ‘signal’ imbedded in a ‘noise’ process, asymptotic normality and independence justifies statistical testing in each cell of the transformed domain of the hypothesis ‘noise alone’ versus the alternate ‘signal plus noise’.

Keywords

NON-UNIFORM SAMPLINGHOMOGENEOUS RANDOM FIELDASYMPTOTIC INDEPENDENCE OF TRANSFORMED VARIABLES
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 1 , March 1975 , pp. 140 - 153
Copyright
Copyright © Applied Probability Trust 1975 

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