Spatial sampling design under the infill asymptotic framework

Environmetrics

Volumn 17, Issue 4, 2006, Pages 323-337

  Zhu, Zhengyuan ^a   Zhang, Hao ^b  

^a The University of North Carolina at Chapel Hill   (United States)

^b WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Infill asymptotics; Maximum likelihood estimation; Simulated annealing; Spatial covariance; Spatial sampling design

Indexed keywords

DESIGN METHOD; SAMPLING;

EID: 33745161073     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.772     Document Type: Article

References (36)

1. Abramowitz M, Stegun I. 1965. Handbook of Mathematical Functions, ninth edn. Dover: New York.
2. Abt M, Welch WJ. 1998. Fisher information and maximum likelihood estimation of covariance parameters in Gaussian stochastic processes. Canadian Journal of Statistics 26: 127-137.
3. Atkinson AC, Donev AN. 1992. Optimum Experimental Designs. Oxford University Press: Oxford, UK.
4. Banjevic M, Switzer P. 2002. Bayesian network designs for fields with variance as a function of the location. Proceedings of the 2002 JSM Conference.
5. Bogaert P, Russo D. 1999. Optimal spatial sampling design for the estimation of the variogram based on a least squares approach. Water Resources Research 35: 1275-1289.
6. Caselton WF, Kan L, Zidek JV. 1992. Quality data networks that minimize entropy. Statistics in the Environmental and Earth Sciences, Walden AT, Guttorp P (eds). Edward Arnold Publishers Ltd: London, Baltimore; 10-38.
7. Chaloner K, Verdinelli I. 1995. Bayesian experimental design: A review. Statistical Science 10: 273-304.
8. Cressie N, Hawkins DM. 1980. Robust estimation of the variogram, I. Journal of the International Association for Mathematical Geology 12: 115-125.
9. Diggle PJ, Ribeiro PJ, Christensen OF. 2002. An introduction to model-based geostatistics. In Spatial Statistics and Computational Methods, Møller J (ed.). Springer-Verlag: New York; 43-86.
10. Geman S, Geman D. 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6: 721-741.
11. Harville DA, Jeske DR. 1992. Mean squared error of estimation or prediction under a general linear model. Journal of the American Statistical Association 87: 724-731.
12. Handcock MS, Wallis JR. 1994. An approach to statistical spatial-temporal modeling of meteorological fields (with discussion). Journal of the American Statistical Association. 89: 368-390.
13. Kirkpatrick S, Gelatt CD, Vecchi MP. 1983. Optimization by simulated annealing. Science 220: 671-680.
14. Ko C, Lee J, Queyranne M. 1995. An exact algorithm for maximum entropy sampling. Operations Research 43: 684-691.
15. Lark R. 2002. Optimized spatial sampling of soil for estimation of the variogram by maximum likelihood. Geoderma 105: 49-80.
16. Mardia KV, Marshall RJ. 1984. Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71: 135-146.
17. Matheron G. 1962. Traite de Geostatistique Appliquee, Tome II: Le Krigeage, Memoires du Bureau de Recherches Geologiques et Minieres, No 24. Edition Technip, Paris.
18. McBratney AB, Webster R, Burgess TM. 1981. The design of optimal sampling schemes for local estimation and mapping of regionalized variables, I - Theory and method. Computers and Geosciences 7: 331-334.
19. Morris MD. 1991. On counting the number of data pairs for semivariogram estimation. Mathematical Geology 23: 929-943.
20. Müller WG, Zimmerman DL. 1999. Optimal designs for variogram estimation. Environmetrics 10: 23-37.
21. Pettitt AN, McBratney AB. 1993. Sampling designs for estimating spatial variance components. Journal of Applied Statistics 42: 185-209.
22. Royle JA. 2002. Exchange algorithms for constructing large spatial designs. Journal of Statistical Planning and Inference 100(2): 121-134.
23. Russo D. 1984. Design of an optimal sampling network for estimating the variogram. Soil Science Society of America Journal 48: 708-716.
24. Stein ML. 1999. Interpolation of spatial data: Some theory for Kriging. Springer-Verlag: New York.
25. Sweeting TJ. 1980. Uniform asymptotic normality of the maximum likelihood estimator (Corr: V10 p320). The Annals of Statistics 8: 1375-1381.
26. van Groenigen JW, Stein A. 1998. Constrained optimization of spatial sampling using continuous simulated annealing. Journal of Environomental Quality 43: 684-691.
27. Warrick AW, Myers DE. 1987. Optimization of sampling locations for variogram calculations. Water Resources Research 23: 496-500.
28. Wiens DP. 2005. Robustness in spatial studies i: Minimax design. Environmetrics 16(2): 191-203.
29. Yfantis EA, Flatman GT, Behar JV. 1987. Efficiency of kriging estimation for square, triangular, and hexagonal grids. Mathematical Geology 19: 183-205.
30. Zhang H. 2004. Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics. Journal of the American Statistical Association 99(465): 250-261.
31. Zhang H, Zimmerman D. 2005. Toward reconciliating two asymptotic frameworks in spatial statisitcs. Biometrika 92(4): (in press).
32. Zhu Z. 2002. Optimal sampling design and parameter estimation of Gaussian random fields. Ph.D thesis, Department of Statistics, the University of Chicago.
33. Zhu Z, Stein M. 2005a. Spatial sampling design for parameter estimation of the covariance function. Journal of Statistical Planning and Inference 134(2): 583-603.
34. Zhu Z, Stein M. 2005b. Two-step spatial sample design for predictiton with estimated parameters. Journal of Agricultural, Biological and Environmental Statistics (in press).
35. Zimmerman DL. 2005. Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction. Environmetrics (in press).
36. Zimmerman DL, Cressie N. 1992. Mean squared prediction error in the spatial linear model with estimated covariance parameters. Annals of the Institute of Statistical Mathematics 44: 27-43.