Anisotropic matérn correlation and spatial prediction using REML

Journal of Agricultural, Biological, and Environmental Statistics

Volumn 12, Issue 2, 2007, Pages 147-160

  Haskard, Kathryn A ^a,b   Cullis, Brian R ^c   Verbyla, Arũnas P ^d  

^a SOUTH AUSTRALIAN RESEARCH AND DEVELOPMENT INSTITUTE   (Australia)

^b ROTHAMSTED RESEARCH   (United Kingdom)

^c NSW DEPARTMENT OF PRIMARY INDUSTRIES   (Australia)

^d UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

Geometric anisotropy; Kriging; Model based geostatistics; Residual maximum likelihood; Spatial correlation

Indexed keywords

CORRELATION; COVARIANCE ANALYSIS; DATA SET; GEOSTATISTICS; KRIGING; MAXIMUM LIKELIHOOD ANALYSIS; NUMERICAL MODEL; PARAMETERIZATION; PH; SALINITY; SOIL; SPATIAL ANALYSIS;

AUSTRALASIA; AUSTRALIA;

EID: 34447309174     PISSN: 10857117     EISSN: 15372693     Source Type: Journal    
DOI: 10.1198/108571107X196004     Document Type: Article

References (21)

1. Abramowitz, M., and Stegun, I. A. (eds.) (1965), Handbook of Mathematical Functions, New York: Dover Publications.
2. Akaike, H. (1973), "Information Theory and an Extension of the Maximum Likelihood Principle," in Proceedings 2nd International Symposium on Information Science, Budapest, eds. B. N. Petrov and F. Csaki, Akademai Kiado, pp. 267-281.
3. Beecher, H. G., Hume, I. H., and Dunn, B. W. (2002), "Improved Method for Assessing Rice Soil Suitability to Restrict Recharge," Australian Journal or Experimental Agriculture, 42, 297-307.
4. Diggle, P. J., Ribeiro, P. J. J., and Christensen, O. F. (2003), "An Introduction to Model-Based Geostatistics," in Spatial Statistics and Computational Methods, ed. J. Møller, New York: Springer, pp. 43-86.
5. Gilmour, A. R., Cullis, B. R., and Verbyla A. P. (1997), "Accounting for Natural and Extraneous Variation in the Analysis of Field Experiments," Journal of Agricultural, Biological and Environmental Statistics, 2, 269-293.
6. Gilmour, A. R., Cullis, B. R., Welham, S. J., Gogel, B. J., and Thompson, R. (2004), "An Efficient Computing Strategy for Prediction in Mixed Linear Models," Computational Statistics and Data Analysis, 44, 571-586.
7. Gilmour, A. R., Gogel, B. J., Cullis, B. R., and Thompson, R. (2005), ASReml User Guide Release 2.0, VSN International Ltd, Hemel Hempstead, HP1 1ES, UK.
8. Gilmour, A. R., Thompson, R., and Cullis, B. R. (1995), "Average Information REML: An Efficient Algorithm for Variance Parameter Estimation in Linear Mixed Models," Biometrics, 51, 1440-1450.
9. Haskard, K. A. (2007), "Anisotropic Matérn Correlation and Other Issues in Model-Based Geostatistics," unpublished Ph. D. thesis, BiometricsSA, University of Adelaide. in preparation.
10. Haskard, K. A., Cullis, B. R., and Verbyla, A. P. (2007), "Estimation and Sampling Issues for an Anisotropic Matérn Correlation Model," submitted.
11. Haskard, K. A., and Verbyla, A. P. (2007), "A Note on an Apparent Non-regular Hypothesis Test," submitted.
12. Kenward, M. G., and Roger, J. H. (1997), "Small Sample Inference for Fixed Effects From Restricted Maximum Likelihood," Biometrics, 53, 983-997.
13. Kitanidis, P. K. (1983), "Statistical Estimation of Polynomial Generalized Covariance Functions and Hydrological Applications," Water Resources Research, 19, 909-921.
14. Lark, R. M., and Cullis, B. R. (2004), "Model-Based Analysis Using REML for Inference from Systematically Sampled Data on Soil," European Journal of Soil Science, 55, 799-813.
15. Matheron, G. (1973), "The Intrinsic Random Functions and their Applications," Journal of Applied Probability, 5, 439-468.
16. Stein, M. L. (1999), Interpolation of Spatial Data: Some Theory for Kriging, New York: Springer-Verlag.
17. Stein, M. L., Chi, Z., and Welty, L. J. (2004), "Approximating Likelihoods for Large Spatial Datasts," Journal of the Royal Statistical Society, Series B, 66, 275-296.
18. Stram, D. O., and Lee, J. W. (1994), "Variance Components Testing in the Longitudinal Mixed Effects Model," Biometrics, 50, 1171-1177.
19. Vecchia, A. V. (1998), "Estimation and Model Identification for Continuous Spatial Processes," Journal of the Royal Statistical Society, Series B, 50, 297-312.
20. Verbyla, A. P. (1990), "A Conditional Derivation of Residual Maximum Likelihood," Australian Journal of Statistics, 32, 227-230.
21. Webster, R., and Oliver, M. A. (2001), Geostatistics for Environmental Scientists, Chichester: Wiley.