Optimal designs for variogram estimation

Environmetrics

Volumn 10, Issue 1, 1999, Pages 23-37

  Müller, Werner G ^a   Zimmerman, Dale L ^b  

^a VIENNA UNIVERSITY OF ECONOMICS AND BUSINESS   (Austria)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

D optimality; Geostatistics; Kriging; Spatial dependence

Indexed keywords

GEOSTATISTICS; VARIOGRAM;

EID: 0345320308     PISSN: 11804009     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-095X(199901/02)10:1<23::AID-ENV333>3.0.CO;2-P     Document Type: Article

References (41)

1. Atkinson, A. C. and Fedorov, V. V. (1975a). 'The design of experiments for discriminating between two rival models'. Biometrika 62, 57-70.
2. Atkinson, A. C. and Fedorov, V. V. (1975b). 'Optimal design: experiments for discriminating between several models'. Biometrika 62, 289-303.
3. Atkinson, A. C. and Haines, L. M. (1996). 'Designs for nonlinear and generalized models'. In Handbook of Statistics, Vol. 13, eds. S. Gosh and C. R. Rao. Amsterdam: Elsevier.
4. Barnes, R. J. (1989). 'Sample design for geologic site characterization'. In Geostatistics, ed. M. Armstrong. Dordrecht: Kluwer, 809-822.
5. Benedetti, R. and Palma, D. (1995). 'Optimal sampling designs for dependent spatial units'. Environmetrics 6, 101-114.
6. Box, G. E. P. and Lucas, H. L. (1959). 'Design of experiments in nonlinear situations'. Biometrika 46, 77-90.
7. Bras, R. L. and Rodriguez-Iturbe, I. (1976). 'Network design for the estimation of areal mean of rainfall events'. Water Resources Research 12, 1185-1195.
8. Brimkulov, U. N., Krug, G. K. and Savanov, V. L. (1980). 'Cislennoje postrojenije tocnych planov eksperimenta pri korrelirovannych izmerenijach'. Zavodskaja Laboratorija (Industrial Laboratory) 46, 435-442.
9. Cox, T. F. and Cox, M. A. A. (1995). Multidimensional Scaling. London: Chapman & Hall.
10. Cressie, N. (1985). 'Fitting variogram models by weighted least squares'. Mathematical Geology 17, 563-586.
11. Cressie, N. and Zimmerman, D. L. (1992). 'On the stability of the geostatistical method'. Mathematical Geology 24, 45-59.
12. Cressie, N., Gotway, C. A. and Grondona, M. O. (1990). 'Spatial prediction from networks'. Chemometrics and Intelligent Laboratory Systems 7, 251-271.
13. Fedorov, V. V. (1972). Theory of Optimal Experiments. New York: Academic Press.
14. Fedorov, V. V. and Flanagan, D. (1998). 'Optimal monitoring network design based on Mercer's expansion of covariance kernel'. Journal of Combinatorics, Information & System Sciences, 23 (at press).
15. Godambe, V. P. and Kale, B. K. (1991). 'Estimating functions: an overview'. In Estimating Functions, ed. V. P. Godambe. Oxford: Clarendon Press, 3-20
16. Graham, W. and McLaughlin, D. (1989a). 'Stochastic analysis of nonstationary subsurface solute transport. 1. Unconditional moments'. Water Resources Research 25(2), 215-232.
17. Graham, W. and McLaughlin, D. (1989b). 'Stochastic analysis of nonstationary subsurface solute transport, 2. Conditional moments'. Water Resources Research 25(11), 2331-2356.
18. Hoeksema, R. J. and Kitanidis, P. K. (1985). 'Analysis of the spatial structure of properties of selected aquifers'. Water Resources Research 21, 563-572.
19. Hunter, W. G. and Reiner, A. M. (1965). 'Designs for discrimination between two rival models'. Technometrics 7, 307-323.
20. Johnson, M. E., Moore, L. M. and Ylvisaker, D. (1990). 'Minimax and maximin distance designs'. Journal of Statistical Planning and Inference 26, 131-148.
21. Lee, S. (1984). 'Multidimensional scaling models with inequality and equality constraints'. Communications in Statistics-Simulation and Computation 13(1), 127-140.
22. Loaiciga, H. A., Charbeneau, R. J., Everett, L. G., Fogg, G. E., Hobbs, B. F. and Rouhani, S. (1992). 'Review of ground-water quality monitoring network design'. Journal of Hydraulic Engineering 118(1), 11-37.
23. Matheron, G. (1963). 'Principles of geostatistics'. Economic Geology 58, 1246-1266.
24. McBratney, A. B., Webster, R. and Burgess, T. M. (1981). 'The design of optimal sampling schemes for local estimation and mapping of regionalized variables - I'. Computers and Geosciences 7, 331-334.
25. Morris, M. D. (1991). 'On counting the number of data pairs for semivariogram estimation'. Mathematical Geology 23, 929-943.
26. Müller, W. G. (1998). 'Least squares fitting from the variogram cloud'. Submitted to Statistics & Probability Letters.
27. Müller, W. G. and Zimmerman, D. L. (1995). 'An algorithm for sampling optimization for semivariogram estimation'. In MODA4 - Advances in Model-Oriented Data Analysis, eds. C. P. Kitsos and W. G. Müller. Heidelberg: Physica, 173-178.
28. Näther, W. (1985). Effective Observations of Random Fields. Teubner Texte zur Mathematik, 72. Leipzig: Teubner Verlag.
29. Pázman, A. (1986). Foundations of Optimum Experimental Design. Dordrecht: Reidel.
30. Pázman, A. and Müller, W. G. (1996). 'Design measures and extended information matrices for optimal designs when the observations are correlated'. TR No. 48, Dept. of Statistics, University of Economics, Vienna.
31. Pettitt, A. N. and McBratney, A. B. (1993). 'Sampling designs for estimating spatial variance components'. Applied Statistics 42(1), 185-209.
32. Pukelsheim, F. (1993). Optimal Design of Experiments. New York: Wiley.
33. Rao, C. R. (1973). Linear Statistical Inference and its Applications, 2nd edn. New York: Wiley.
34. Robinson, G. K. (1990). 'A role for variograms'. Australian Journal of Statistics 32, 327-335.
35. Russo, D. (1984). 'Design of an optimal sampling network for estimating the variogram'. Soil Science Society of American Journal 48, 708-716.
36. Sacks, J. and Ylvisaker, D. (1966). 'Designs for regression problems with correlated errors'. Ann. Math. Statist. 37, 66-89.
37. Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P. (1989). 'Design and analysis for computer experiments'. Statistical Science 4, 409-423.
38. Stein, M. L. (1988). 'Asymptotically efficient prediction of a random field with a misspecified covariance function'. Annals of Statistics 16, 55-63.
39. Warrick, A. W. and Myers, D. E. (1987). 'Optimization of sampling locations for variogram calculations'. Water Resources Research 23, 496-500.
40. Yfantis, E. A., Flatman, G. T. and Behar, J. V. (1987). 'Efficiency of kriging estimation for square, triangular, and hexagonal grids'. Mathematical Geology 19, 183-205.
41. Zimmerman, D. L. and Homer, K. E. (1991). 'A network design criterion for estimating selected attributes of the semivariogram'. Environmetrics 2(4), 425-441.