Efficient computation of maximum likelihood estimators in a spatial linear model with power exponential covariogram

Computers and Geosciences

Volumn 27, Issue 1, 2001, Pages 1-7

  Park, Jeong Soo ^a   Baek, Jangsun ^a  

^a Chonnam National University   (South Korea)

Author keywords

Cholesky decomposition; Gaussian processes; Geostatistics; Gradient; Quasi Newton optimization

Indexed keywords

EID: 0033794656     PISSN: 00983004     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0098-3004(00)00016-9     Document Type: Article

References (19)

1. Abt, M., Welch, W., Sacks, J., 1999. Design and analysis for modeling and predicting spatial contamination. Mathematical Geology 31 (1), 1-22.
2. Bates, R., Buck, R., Riccomagno, E., Wynn, H., 1996. Experimental design and observation for large systems. Journal of Royal Statistical Society, Series B 58 (1), 77-94.
3. Cressie, N., 1991. Statistics for Spatial Data. John Wiley, New York 900 pp.
4. Davis, J.C., 1986. Statistics and Data Analysis in Geology, 2nd ed. John Wiley, New York 646 pp.
5. Diggle, P.J., Tawn, J.A., Moyeed, R.A., 1998. Model-based geostatistics (with discussion). Journal of Royal Statistical Society, Series C: Applied Statistics 47 (3), 299-350.
6. Dongarra, J., Moler, C., Bunch, J., Stewart, G., 1979. LINPACK User's Guide. SIAM, Philadelphia 357 pp.
7. Gao, F., Sacks, J., Welch, W., 1996. Predicting urban ozone levels and trends with semiparametric modeling. Journal of Agricultural, Biological, and Environmental Statistics 1 (4), 404-425.
8. IMSL, 1987. User's Manual Math/Library Version 1.0, vol. 3, IMSL Houston (1150 pp).
9. Kitanidis, P., Lane, R., 1985. Maximum likelihood parameter estimation of hydrologic spatial processes by the Gauss-Newton method. Journal of Hydrology 79 (1/2), 53-71.
10. Mardia, K., Marshall, R., 1984. Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71 (1), 135-146.
11. Pardo-Igúzquiza, E., 1997. MLREML; a computer, program for the inference of spatial covariance parameters by maximum likelihood and restricted maximum likelihood. Computers and Geosciences 23 (2), 153-162.
12. Pardo-Igúzquiza, E., 1998a. Maximum likelihood estimation of spatial covariance parameters. Mathematical Geology 30 (1), 95-108.
13. Pardo-Igúzquiza, E., 1998b. MLREML4: a program for the inference of the power variogram model by maximum likelihood and restricted maximum likelihood. Computers and Geosciences 24 (6), 537-543.
14. Peressini, A.L., Sullivan, F.E., Uhl Jr, J.J., 1988. The Mathematics of Nonlinear Programming. Springer-Verlag, New York 273 pp.
15. Ripley, B.D., 1981. Spatial Statistics. John Wiley, New York 252 pp.
16. Sacks, J., Welch, W., Mitchell, T., Wynn, H., 1989. Design and analysis of computer experiment (with discussion). Statistical Science 4 (4), 409-435.
17. Searle, S., 1982. Matrix Algebra Useful for Statistics. John Wiley, New York 438 pp.
18. Vecchia, A., 1988. Estimation and model identification for continuous spatial processes. Journal of the Royal Statistical Society, Series B 50 (2), 297-312.
19. Welch, W.J., Buck, R.J., Sacks, J., Wynn, H.P., Mitchell, T.J., Morris, M.D., 1992. Screening, predicting, and computer experiments. Technometrics 34 (1), 15-25.