On Prediction Properties of Kriging: Uniform Error Bounds and Robustness

References

• Adler, R. J., and Taylor, J. E. (2009), Random Fields and Geometry, New York: Springer Science & Business Media.
   Google Scholar
• Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004), Hierarchical Modeling and Analysis for Spatial Data, Boca Raton, FL: CRC Press, Taylor & Francis Group.
   Google Scholar
• Buslaev, A., and Seleznjev, O. (1999), “On Certain Extremal Problems in the Theory of Approximation of Random Processes,” East Journal on Approximations, 5, 467–481.
   Google Scholar
• Cramér, H., and Leadbetter, M. R. (1967), Stationary and Related Stochastic Processes: Sample Function Properties and Their Applications, Mineola, NY: Courier Corporation.
   Google Scholar
• Fan, J., and Gijbels, I. (1996), Local Polynomial Modeling and Its Applications: Monographs on Statistics and Applied Probability (Vol. 66), Boca Raton, FL: CRC Press.
   Google Scholar
• Jiang, J., Nguyen, T., and Rao, J. S. (2011), “Best Predictive Small Area Estimation,” Journal of the American Statistical Association, 106, 732–745. DOI: 10.1198/jasa.2011.tm10221.
   Web of Science ®Google Scholar
• Johnson, M. E., Moore, L. M., and Ylvisaker, D. (1990), “Minimax and Maximin Distance Designs,” Journal of Statistical Planning and Inference, 26, 131–148. DOI: 10.1016/0378-3758(90)90122-B.
   Web of Science ®Google Scholar
• Matheron, G. (1963), “Principles of Geostatistics,” Economic Geology, 58, 1246–1266. DOI: 10.2113/gsecongeo.58.8.1246.
   Google Scholar
• Pollard, D. (1990), “Empirical Processes: Theory and Applications,” in NSF-CBMS Regional Conference Series in Probability and Statistics, JSTOR, pp. i–86.
   Google Scholar
• Rao, J. N. K., and Molina, I. (2015), Small-Area Estimation, Hoboken, NJ: Wiley.
   Google Scholar
• Rasmussen, C. E. (2006), Gaussian Processes for Machine Learning, Cambridge, MA: MIT Press.
   Google Scholar
• Ritter, K. (2000), Average-Case Analysis of Numerical Problems, Berlin, Heidelberg: Springer.
   Google Scholar
• Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), “Design and Analysis of Computer Experiments,” Statistical Science, 4, 409–423. DOI: 10.1214/ss/1177012413.
   Google Scholar
• Santner, T. J., Williams, B. J., and Notz, W. I. (2003), The Design and Analysis of Computer Experiments, New York: Springer Science & Business Media.
   Google Scholar
• Stein, M. L. (1988), “Asymptotically Efficient Prediction of a Random Field With a Misspecified Covariance Function,” The Annals of Statistics, 16, 55–63. DOI: 10.1214/aos/1176350690.
   Web of Science ®Google Scholar
• Stein, M. L. (1990a), “Bounds on the Efficiency of Linear Predictions Using an Incorrect Covariance Function,” The Annals of Statistics, 18, 1116–1138. DOI: 10.1214/aos/1176347742.
   Web of Science ®Google Scholar
• Stein, M. L. (1990b), “Uniform Asymptotic Optimality of Linear Predictions of a Random Field Using an Incorrect Second-Order Structure,” The Annals of Statistics, 18, 850–872. DOI: 10.1214/aos/1176347629.
   Web of Science ®Google Scholar
• Stein, M. L. (1993), “A Simple Condition for Asymptotic Optimality of Linear Predictions of Random Fields,” Statistics & Probability Letters, 17, 399–404. DOI: 10.1016/0167-7152(93)90261-G.
   Web of Science ®Google Scholar
• Stein, M. L. (1999), Interpolation of Spatial Data: Some Theory for Kriging, New York: Springer Science & Business Media.
   Google Scholar
• Tuo, R., and Wu, C. F. J. (2015), “Efficient Calibration for Imperfect Computer Models,” The Annals of Statistics, 43, 2331–2352. DOI: 10.1214/15-AOS1314.
   Web of Science ®Google Scholar
• van der Vaart, A. W., and van Zanten, J. H. (2008), “Reproducing Kernel Hilbert Spaces of Gaussian Priors,” in Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, Beachwood, OH: Institute of Mathematical Statistics, pp. 200–222.
   Google Scholar
• van der Vaart, A. W., and Wellner, J. A. (1996), Weak Convergence and Empirical Processes, New York: Springer.
   Google Scholar
• Wahba, G. (1990), Spline Models for Observational Data (Vol. 59), Philadelphia, PA: SIAM.
   Google Scholar
• Wendland, H. (2004), Scattered Data Approximation (Vol. 17), Cambridge, UK: Cambridge University Press.
   Google Scholar
• Wu, C. F. J., and Hamada, M. S. (2009), Experiments: Planning, Analysis, and Optimization (2nd ed.), New York: Wiley.
   Google Scholar
• Wu, Z., and Schaback, R. (1993), “Local Error Estimates for Radial Basis Function Interpolation of Scattered Data,” IMA Journal of Numerical Analysis, 13, 13–27. DOI: 10.1093/imanum/13.1.13.
   Web of Science ®Google Scholar
• Xiu, D. (2010), Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton, NJ: Princeton University Press.
   Google Scholar
• Yakowitz, S., and Szidarovszky, F. (1985), “A Comparison of Kriging With Nonparametric Regression Methods,” Journal of Multivariate Analysis, 16, 21–53. DOI: 10.1016/0047-259X(85)90050-8.
   Web of Science ®Google Scholar
• Ying, Z. (1991), “Asymptotic Properties of a Maximum Likelihood Estimator With Data From a Gaussian Process,” Journal of Multivariate Analysis, 36, 280–296. DOI: 10.1016/0047-259X(91)90062-7.
   Web of Science ®Google Scholar
• Zhang, H. (2004), “Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics,” Journal of the American Statistical Association, 99, 250–261. DOI: 10.1198/016214504000000241.
   Web of Science ®Google Scholar