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On the variance of the sample correlation between two independent lattice processes

Published online by Cambridge University Press:  14 July 2016

Sylvia Richardson  and
Denis Hemon
Sylvia Richardson*
Affiliation:
Institut National de la Santé et de la Recherche Médicale
Denis Hemon*
Affiliation:
Institut National de la Santé et de la Recherche Médicale
*
∗Postal address: U170 Statistiques, 16 bis avenue Paul Vaillant Couturier, 94800 Villejuif, France.
∗Postal address: U170 Statistiques, 16 bis avenue Paul Vaillant Couturier, 94800 Villejuif, France.
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Abstract

Consider two stochastically independent, stationary Gaussian lattice processes with zero means, {X(u), u (Z2} and {Y(u), u (Z2}. An asymptotic expression for the variance of the sample correlation between {X(u)} and {Y(u)} over a finite square is derived. This expression also holds for a wide class of domains in Z2. As an illustration, the asymptotic variance of the correlation between two first-order autonormal schemes is evaluated.

Keywords

AUTONORMAL SCHEMESLATTICE PROCESSESSAMPLE CROSS-CORRELATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 943 - 948
Copyright
Copyright © Applied Probability Trust 1981 

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