A formal test for nonstationarity of spatial stochastic processes

Journal of Multivariate Analysis

Volumn 96, Issue 1, 2005, Pages 30-54

  Fuentes, Montserrat ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Anisotropy; Covariance; Fourier transform; Geostatistics; Periodogram; Spatial statistics; Tapering; Variogram

Indexed keywords

EID: 23844472403     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmva.2004.09.003     Document Type: Article

References (31)

1. S. Bose A.O. Steinhardt Invariant tests for spatial stationarity using covariance structure IEEE Trans. Signal Process. 44 1996 1523-1533
2. D.R. Brillinger, The frequency analysis of relations between stationary spatial series, in: R. Pyke (Ed.), Proceedings of the Twelfth Biennial Seminar of the Canadian Mathematical Congress, Montreal, Canadian Math. Congress, 1970, pp. 39-81.
3. D.R. Brillinger, Time Series: Data Analysis and Theory, Expanded edition, Holden-Day, Inc, San Francisco, 1981.
4. A.G. Constantine P. Hall Characterizing surface smoothness via estimation of effective fractal dimension J. Roy. Statist. Soc. Ser. B 56 1994 97-113
5. H. Cramér, On some classes of non-stationary processes, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistical and Probability, Vol. 2, University of California Press, Berkeley, CA, 1960, pp. 57-78.
6. N. Cressie Statistics for Spatial Data 1993 Wiley New York
7. R. Dahlhaus On the Kullback-Leibler information divergence of locally stationary processes Stochastics Process. Appl. 62 1996 139-168
8. R. Dahlhaus, Asymptotic statistical inference for nonstationary processes with evolutionary spectra, in: P.M. Robinson, M. Rosenblatt (Eds.), Athens Conference on Applied Probability and Time Series, Vol II, Lecture Notes in Statistics 115, Springer, New York, 1996, pp. 145-159.
9. R. Dahlhaus, M. Sahm, Local likelihood methods for nonstationary time series and random fields, Technical report, Universität Heidelberg, 2001.
10. A. Ephraty J. Tabrikian H. Messer Underwater source detection using a spatial stationary test J. Acoust. Soc. Amer. 109 2001 1053-1063
11. M. Fuentes Spectral methods for nonstationary spatial processes Biometrika 89 2002 197-210
12. M. Fuentes, A. Raftery, Model evaluation and spatial interpolation by Bayesian combination of observations with Outputs from Numerical Models, Biometrics, 2004, in press.
13. P. Guttorp W. Meiring P. Sampson A space-time analysis of ground-level ozone data Environmetrics 5 1994 241-254
14. P. Guttorp P. Sampson Methods for estimating heterogeneous spatial covariance functions with environmental applications in: G.P. Patil C.R. Rao (Eds.), Handbook of Statistics 12 1994 Elsevier Science B.V. Amsterdam 661-689
15. X. Guyon Parameter estimation for a stationary process on a d-dimensional lattice Biometrika 69 1982 95-105
16. X. Guyon Champs Aléatoires sur un Réseau 1992 Masson Paris
17. D. Higdon J. Swall J. Kern Non-stationary spatial modeling in: J.M. Bernardo (Ed.), Bayesian Statistics 6 1999 Oxford University Press Oxford 761-768
18. G.M. Jenkins General considerations in the estimation of spectra Technometrics 3 1961 133-166
19. Y. Pawitan F. O'Sullivan Nonparametric spectral density estimation using penalized Whittle likelihood J. Amer. Statist. Assoc. 89 1994 600-610
20. M.B. Priestley Evolutionary spectral and nonstationary processes J. Roy. Statist. Soc. Ser. B 27 1965 204-237
21. M.B. Priestley Design relations for non-stationary processes J. Roy. Statist. Soc. Ser. B 28 1966 228-240
22. M.B. Priestley T.S. Rao A test for non-stationarity of time-series J. Roy. Statist. Soc. Ser. B 31 1969 140-149
23. B.D. Ripley Spatial Statistics 1981 Wiley New York
24. M.R. Rosenblatt Stationary Sequences and Random Fields 1985 Birkhäuser Boston
25. P.D. Sampson P. Guttorp Nonparametric estimation of nonstationary spatial covariance structure J. Amer. Statist. Assoc. 87 1992 108-119
26. R.L. Smith Estimating nonstationary spatial correlations 1996 Preprint University of North Carolina
27. S.K. Stein Calculus in the first three dimensions 1967 McGraw-Hill, Inc New York
28. M.L. Stein Fixed-domain asymptotics for spatial periodograms J. Amer. Statist. Assoc. 90 1995 1277-1288
29. M.L. Stein Interpolation of Spatial Data: Some Theory for Kriging 1999 Springer New York
30. P. Whittle On stationary processes in the plane Biometrika 41 1954 434-449
31. A.M. Yaglom Correlation Theory of Stationary and Related Random Functions 1987 Springer New York