Estimating the prediction mean squared error in gaussian stochastic processes with exponential correlation structure

Scandinavian Journal of Statistics

Volumn 26, Issue 4, 1999, Pages 563-578

  Abt, Markus ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Computer experiments; Exponential covariance; Gaussian stochastic process; Information matrix; Kriging; Mean squared error; Spatial linear model; Spatial statistics

Indexed keywords

EID: 0033242689     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00168     Document Type: Article

References (21)

1. Abt, M. (1998). Approximating the mean squared prediction error in linear models under the family of exponential correlations. Statist. Sinica 8, 511-526.
2. Abt, M. & Welch, W. J. (1998). Fisher information and maximum likelihood estimation of covariance parameters in Gaussian stochastic processes. Canad. J. Statist. 26, 127-137.
3. Abt, M., Welch, W. J. & Sacks, J. (1998). Prediction of log-Gaussian processes and application to a cleanup scheme for environmental contaminations, unpublished manuscript.
4. Abt, M., Welch, W. J. & Sacks, J. (1999). Design and analysis for modeling and predicting spatial contamination. Math. Geol. 31, 1.
5. Aptech (1996). GAUSS mathematical and statistical system, system and graphics manual: version 3.2.33. Apech Systems, Maple Valley, WA.
6. Belyaev, Yu. K. (1959). Analytic random processes. Theory Probab. Appl. 4, 402-409.
7. Gao, F., Sacks, J. & Welch, W. J. (1996). Predicting urban ozone levels and trends with semiparametric modelling. J. Agricultural Biol. Environ. Statist. 1, 404-425.
8. Haaland, P., McMillan, N. J., Nychka, D. & Welch, W. J. (1994). Analysis of space-filling designs. Comput. Sci. Statist. 26, 111-120.
9. Harville, D. A. & Jeske, D. R. (1992). Mean squared error of estimation or prediction under a general linear model. J. Amer. Statist. Assoc. 87, 724-731.
10. Ibragimov, I. A. & Rozanov, Y. A. (1978). Gaussian random processes. Springer, New York.
11. Johnson, M. E., Moore, L. M. & Ylvisaker, D. (1990). Minimax and maximin distance designs. J. Statist. Plann. Inference 26, 131-148.
12. Jones, D. R., Schonlau, M. & Welch, W. J. (1998). Efficient global optimization of expensive black-box functions, J. Global Optim. 13, 455-492.
13. Kackar, R. N. & Harville, D. A. (1984). Approximations for standard errors of estimators of fixed and random effects in mixed linear models. J. Amer. Statist. Assoc. 79, 853-862.
14. McMillan, N. J., Sacks, J., Welch, W. J. & Gao, F. (1999). Analysis of protein activity data by Gaussian stochastic process models. J. Biopharm. Statist. 9, to appear.
15. Moran, P. A. P. (1971). Maximum-likelihood estimation in non-standard conditions. Proc. Cambridge Philos. Soc. 70, 441-450.
16. Schonlau, M. (1997). Computer experiments and global optimization. PhD dissertation, University of Waterloo, Canada.
17. Schott, J. R. (1997). Matrix analysis for statistics. Wiley, New York.
18. Welch, W. J. (1995a). ACED (Algorithms for the Construction of Experimental Designs), version 2.01 beta, unpublished software.
19. Welch, W. J. (1995b). GaSP (Gaussian Stochastic Process), version 2.02 beta, unpublished software.
20. 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, 15-25.
21. Zimmerman, D. L. & Cressie, N. (1992). Mean squared prediction error in the spatial linear model with estimated covariance parameters. Ann. Inst. Statist. Math. 44, 27-43.