A nonparametric assessment of properties of space-time covariance functions

Journal of the American Statistical Association

Volumn 102, Issue 478, 2007, Pages 736-744

  Li, Bo ^a   Genton, Marc G ^b   Sherman, Michael ^c  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^b UNIVERSITY OF GENEVA   (Switzerland)

^c TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Asymptotic normality; Covariance; Full symmetry; Random field; Separability; Stationarity

Indexed keywords

EID: 34250783936     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214507000000202     Document Type: Article

References (29)

1. Carlstein, E. (1986), "The Use of Subseries Values for Estimating the Variance of a General Statistic From a Stationary Sequence," The Annals of Statistics, 14, 1171-1179.
2. Cox, D. R., and Isham, V. (1988), "A Simple Spatial-Temporal Model of Rain-fall," Proceedings of the Royal Society of London, Ser. A, 415, 317-328.
3. Cressie, N. (1993), Statistics for Spatial Data, New York: Wiley.
4. Cressie, N., and Huang, H.-C. (1999), "Classes of Nonseparable, SpatioTemporal Stationary Covariance Functions," Journal of the American Statistical Association, 94, 1330-1340.
5. de Luna, X., and Genton, M. G. (2005), "Predictive Spatio-Temporal Models for Spatially Sparse Environmental Data," Statistica Sinica, 15, 547-568.
6. Fuentes, M. (2006), "Testing for Separability of Spatial-Temporal Covariance Functions," Journal of Statistical Planning & Inference, 136, 447-466.
7. Gneiting, T. (2002), "Nonseparable, Stationary Covariance Functions for Space-Time Data," Journal of the American Statistical Association, 97, 590-600.
8. Gneiting, T., Genton, M. G., and Guttorp, P. (2007), "Geostatistical Space-Time Models, Stationarity, Separability and Full Symmetry," in Statistics of Spatio-Temporal Systems, Vol. 107, eds. B. Finkenstaedt, L. Held, and V. Isham, Boca Raton, FL: Chapman & Hall/CRC Press, pp. 151-175.
9. Guan, Y., Sherman, M., and Calvin, J. A. (2004), "A Nonparametric Test for Spatial Isotropy Using Subsampling," Journal of the American Statistical Association, 99, 810-821.
10. Hall, P., Fisher, N. I., and Hoffmann, B. (1994), "On the Nonparametric Estimation of Covariance Functions," The Annals of Statistics, 22, 2115-2134.
11. Haslett, J., and Raftery, A. E. (1989), "Space-Time Modelling With Long-Memory Dependence: Assessing Ireland"s Wind-Power Resource" (with discussion), Applied Statistics, 38, 1-50.
12. Ibragimov, I. A., and Linnik, Y. V. (1971), Independent and Stationary Sequences of Random Variables, Gronigen, The Netherlands: Wolters-Noordhoff Publishing.
13. Jun, M., and Stein, M. L. (2007), "An Approach to Producing Space-Time Covariance Functions on Spheres," Technometrics, in press.
14. Künsch, H. (1989), "The Jackknife and Bootstrap for General Stationary Observations," The Annals of Statistics, 17, 1217-1241.
15. Lahiri, S. N. (2003), Resampling Methods for Dependent Data, New York: Springer-Verlag.
16. Lu, H., and Zimmerman, D. L. (2001), "Testing for Isotropy and Other Directional Symmetry Properties of Spatial Correlation," preprint.
17. _ (2005), "Testing for Directional Symmmetry in Spatial Dependence Using the Periodogram," Journal of Statistical Planning & Inference, 129, 369-385.
18. Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979), Multivariate Analysis, New York: Academic Press.
19. Mitchell, M. W., Genton, M. G., and Gumpertz, M. L. (2005), "Testing for Separability of Space-Time Covariances," Environmetrics, 16, 819-831.
20. _ (2006), "A Likelihood Ratio Test for Separability of Covariances," Journal of Multivariate Analysis, 97, 1025-1043.
21. Priestley, M. B. (1981), Spectral Analysis and Time Series, London: Academic Press.
22. Scaccia, L., and Martin, R. J. (2002), "Testing for Simplification in Spatial Models, in COMPSTAT 2002, Heidelberg: Physica, pp. 581-586.
23. _ (2005), "Testing Axial Symmetry and Separability of Lattice Processes," Journal of Statistical Planning & Inference, 131, 19-39.
24. Sherman, M. (1996), "Variance Estimation for Statistics Computed From Spatial Lattice Data," Journal of the Royal Statistical Society, Ser. B, 58, 509-523.
25. Stein, M. (1999), Interpolation of Spatial Data: Some Theory for Kriging, New York: Springer-Verlag.
26. _ (2005), "Space-Time Covariance Functions," Journal of the American Statistical Association, 100, 310-321.
27. Stol, P. T. (1983), "Rainfall Interstation Correlation Functions: VII. On Non-Monotonousness," Journal of Hydrology, 64, 69-92.
28. Taylor, G. I. (1938), "The Spectrum of Turbulence," Proceedings of the Royal Society of London, Ser. A, 164, 476-490.
29. Wikle, C. K., and Cressie, N. (1999), "A Dimension-Reduction Approach to Space-Time Kalman Filtering," Biometrika, 86, 815-829.