Least squares variogram fitting by spatial subsampling

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 64, Issue 4, 2002, Pages 837-854

  Lee, Yoon Dong ^a   Lahiri, Soumendra N ^b  

^a Seoul National University   (South Korea)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

Generalized least squares estimator; Increasing domain asymptotics; Spatial regression

Indexed keywords

EID: 0036436129     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00364     Document Type: Article

References (25)

1. Barry, J., Crowder, M. and Diggle, P. (1997) Parametric estimation of the variogram. Preprint. Department of Mathematics and Statistics. Lancaster University, Lancaster.
2. Bradley, R.C. (1993) Equivalent mixing conditions for random fields. Ann. Probab., 21, 1921-1926.
3. Cressie, N. (1985) Fitting variogram models by weighted least squares. J. Int. Ass. Math. Geol., 17, 693-702.
4. _(1993) Statistics for Spatial Data, 2nd edn. New York: Wiley.
5. David, M. (1977) Geostatistical Ore Reserve Estimation. Amsterdam: Elsevier.
6. Dennis, J.E. and Schnabel, R.B. (1983) Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Englewood Cliffs: Prentice Hall.
7. Doukhan, P. (1994) Mixing: Properties and Examples. New York: Springer.
8. Genton, M.G. (1997) Variogram fitting by generalized least squares using an explicit formula for the covariance structure. Preprint. Massachusetts Institute of Technology, Cambridge.
9. Hall, P. and Jing, B. (1996) On sample reuse methods for dependent data. J. R. Statist. Soc. B, 58, 727-737.
10. Journel, A.G. and Huijbregts, C.J. (1978) Mining Geostatistics. London: Academic Press.
11. Künsch, H. (1989) The jackknife and the bootstrap for general stationary observations. Ann. Statist., 17, 1217-1241.
12. Lahiri, S.N. (2002) Central limit theorems for weighted sums of a spatial process under a class of stochastic and fixed designs. Sankhya A, to be published.
13. Lahiri, S.N., Kaiser, M.S., Cressie, N. and Hsu, N.-J. (1999) Prediction of spatial cumulative distribution functions using subsampling (with discussion). J. Am. Statist. Ass., 94, 86-110.
14. Lahiri, S., Lee, Y. and Cressie, N. (2002) Efficiency of least squares estimators of spatial variogram parameters. J. Statist. Planng Inf., to be published.
15. Matheron, G. (1962) Traité de geostatistique appliquée, tome I. Mem. Bur. Rec. Geol. Min., 14.
16. Meijia, J.M. and Rodriguez-Iturbe, I. (1974) On the synthesis of random field sampling from the spectrum: an application to the generation of hydrologic spatial processes. Wat. Resour. Res., 10, 705-711.
17. Mercer, W.B. and Hall, A.D. (1911) The experimental error of field trials. J. Agric. Sci. Camb., 4, 107-132.
18. Politis, D. and Romano, J.P. (1992) A general sampling scheme for triangular arrays of α-mixing random variables with application to the problem of spectral density estimation. Ann. Statist., 20, 1985-2007.
19. _(1993) Nonparametric resampling for homogeneous strong mixing random fields. J. Multiv. Anal., 47, 301-328.
20. _(1994) Large sample confidence regions based on subsamples under minimal assumptions. Ann. Statist., 22, 2031-2050.
21. Possolo, A. (1991) Subsampling a random field. In Spatial Statistics and Imaging (ed. A. Possolo), pp. 286-294. Hayward: Institute of Mathematical Statistics.
22. Sherman, M. (1996) Variance estimation for statistics computed from spatial lattice data. J. R. Statist. Soc. B, 58, 509-523.
23. Sherman, M. and Carlstein, E. (1994) Nonparametric estimation of the moments of a general statistic computed from spatial data. J. Am. Statist. Ass., 89, 496-500.
24. Shinozuka, M. (1971) Simulation of multivariate and multidimensional random processes. J. Acoust. Soc. Am., 49, 357-367.
25. Zhang, X., van Eijkeren, J. and Heemink, A. (1995) On the weighted least-squares method for fitting a semivariogram model. Comput. Geosci., 21, 605-608.