Nonstationary covariance models for global data

Annals of Applied Statistics

Volumn 2, Issue 4, 2008, Pages 1271-1289

  Jun, Mikyoung ^a   Stein, Michael L ^a  

^a NONE

Author keywords

Fast Fourier transform; Nonstationary covariance function; Processes on spheres; TOMS ozone data

Indexed keywords

EID: 78751616255     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/08-AOAS183     Document Type: Article

References (28)

1. Anderes, E. B. and Stein, M. L. (2008). Estimating deformations of isotropic Gaussian random fields on the plane. Ann. Statist. 36 719-741.
2. Caragea, P. and Smith, R. L. (2006). Approximate likelihoods for spatial processes. Technometrics. To appear.
3. Clerc, M. and Mallat, S. (2003). Estimating deformations of stationary processes. Ann. Statist. 31 1772-1821.
4. Cressie, N. and Johannesson, G. (2008). Fixed rank kriging for very large spatial data sets. J. Roy. Statist. Soc. Ser. B 70 209-226.
5. Das, B. (2000). Global covariance modeling: A deformation approach to anisotropy. Unpublished Ph.D. dissertation, Univ. Washington.
6. Davis, P. J. (1979). Circulant Matrices. Wiley, New York.
7. Fang, D. and Stein, M. L. (1998). Some statistical methods for analyzing the TOMS data. J. Geophys. Res. 103 26165-26182.
8. Fuentes, M. (2002). Spectral methods for nonstationary spatial processes. Biometrika 89 197-210.
9. Fuentes, M. (2007). Approximate likelihood for large irregularly spaced spatial data. J. Amer. Statist. Assoc. 102 321-331.
10. Gneiting, T. (1999). Correlation functions for atmospheric data analysis. Quarterly J. Roy. Meteorological Soc. 125 2449-2464.
11. Higdon, D. (1998). A process-convolution approach to modeling temperatures in the North-Atlantic Ocean. Environ. Ecol. Stat. 5 173-190.
12. Higdon, D. M., Swall, J. and Kern, J. (1999). Non-stationary spatial modeling. In Bayesian Statistics 6 761-768. Oxford Univ. Press.
13. Holton, J. R. (1992). An Introduction to Dynamic Meteorology, 3rd ed., 216-222. Academic Press, New York.
14. Jones, R. H. (1963). Stochastic processes on a sphere. Ann. Math. Statist. 34 213-218.
15. Jun, M. and Stein, M. L. (2007). An approach to producing space-time covariance functions on spheres. Technometrics 49 468-479.
16. Krueger, A. J., Bhartia, P. K., McPeters, R. D., Herman, J. R., Wellemeyer, C. G., Jaross, G., Seftor, C. J., Torress, O., Labow, G., Byerly, W., Taylor, S. L., Swissler, T. and Cebual, R. P. (1998). ADEOS total ozone mapping spectrometer (TOMS) data products users guide. Greenbelt, MD: National Aeronautics and Space Administration. Available at toms.gsfc.nasa.gov/datainfo/adeos_userguide.pdf.
17. Nychka, D., Wikle, C. and Royle, K. A. (2002). Multiresolution models for nonstationary spatial covariance functions. Stat. Model. 2 315-332.
18. Paciorek, C. and Schervish, M. (2006). Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 17 483-506.
19. Perrin, O. and Senoussi, R. (2000). Reducing non-stationary random fields to stationarity and isotropy using a space deformation. Statist. Probab. Lett. 48 23-32.
20. Sampson, P. D. and Guttorp, P. (1992). Nonparametric estimation of nonstationary spatial covariance structure. J. Amer. Statist. Assoc. 87 108-119.
21. Schmidt, A. M. and O'Hagan, A. (2003). Bayesian inference for non-stationary spatial covariance structure via spatial deformations. J. Roy. Statist. Soc. Ser. B 65 743-758.
22. Stein, M. L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. Springer, New York.
23. Stein, M. L. (2007). Spatial variation of total column ozone on a global scale. Ann. Appl. Statist. 1 191-210.
24. Stein, M. L. (2008). A modeling approach for large spatial datasets. J. Korean Statist. Soc. 37 3-10.
25. Stein, M. L., Chi, Z. and Welty, L. J. (2004). Approximating the likelihood for irregularly observed Gaussian random fields. J. Roy. Statist. Soc. Ser. B 66 275-296.
26. Tukey, J. W. (1967). An introduction to the calculations of numerical spectrum analysis. In Advanced Seminar on Spectral Analysis of Time Series (B. Harris, ed.) 25-46. Wiley, New York.
27. Vecchia, A. V. (1988). Estimation and model identification for continuous spatial processes. J. Roy. Statist. Soc. Ser. B 50 297-312.
28. Yaglom, A. M. (1987). Correlation Theory of Stationary and Related Random Functions. I. Springer, New York.