Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-22T05:35:12.534Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Bartlett, M. S. (1935) Some aspects of the time-correlation problem in regard to tests of significance. J. R. Statist. Soc. 98, 536–543.Google Scholar
Bartlett, M. S. (1966) An Introduction to Stochastic Processes , 2nd edn. Cambridge University Press.Google Scholar
Bennett, R. J. (1980) Spatial Time Series. Pion, London.Google Scholar
Besag, J. E. (1972) On the correlation structure of some two-dimensional stationary processes. Biometrika 59, 43–48.Google Scholar
Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion). J. R. Statist. Soc. B 36, 192–236.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
Haugh, L. D. and Box, G. E. P. (1977) Identification of dynamic regression (distributed lag) models connecting two time series. J. Amer. Statist. Assoc. 72, 121–130.Google Scholar
Moran, P. A. P. (1973a) A Gaussian Markovian process on a square lattice. J. Appl. Prob. 10, 54–62.Google Scholar
Moran, P. A. P. (1973b) Necessary conditions for Markovian processes on a lattice. J. Appl. Prob. 10, 605–612.Google Scholar
Pierce, D. A. (1979) R2 measures for time series J. Amer. Statist. Assoc. 74, 901–910.Google Scholar
Quenouille, M. H. (1947) Notes on the calculation of autocorrelations of linear autoregressive schemes. Biometrika 34, 365–367.Google Scholar
Rozanov, Yu. A. (1967) On the Gaussian homogeneous fields with given conditional distributions. Theory Prob. Appl. 12, 381–391.Google Scholar
Tjøstheim, D. (1978) Statistical spatial series modelling. Adv. Appl. Prob. 10, 130–154.CrossRefGoogle Scholar
Whittle, P. (1954) On stationary processes in the plane. Biometrika 41, 434–449.CrossRefGoogle Scholar