References
- Anitescu, M., Chen, J., and Wang, L. (2012), “A Matrix-Free Approach for Solving the Gaussian Process Maximum Likelihood Problem,” SIAM Journal on Scientific Computing, 34, 240–262.
- Aune, E., Simpson, D., and Eidsvik, J. (2013), “Parameter Estimation in High Dimensional Gaussian Distributions,” Journal of Statistics and Computing, 24, 247–263.
- Caragea, P. (2003), “Approximate Likelihoods for Spatial Processes,” Ph.D. dissertation, University of North Carolina at Chapel Hill.
- Chen, K. (2005), Matrix Preconditioning Techniques and Applications, Cambridge, UK: Cambridge University Press.
- Fang, K.F., Li, R.Z., and Sudjianto, A. (2005), Design and Modeling for Computer Experiments, New York: Chapman & Hall/CRC Press.
- Fuentes, M. (2007), “Approximate Likelihood for Large Irregularly Spaced Spatial Data,” Journal of the American Statistical Association, 102, 321–331.
- Furrer, R., Genton, M.G., and Nychka, D. (2006), “Covariance Tapering for Interpolation of Large Spatial Datasets,” Journal of Computational and Graphical Statistics, 15, 502–523.
- Genton, M.G. (2007), “Separable Approximations of Space-Time Covariance Matrices,” Environmetrics, 18, 681–695.
- Gneiting, T., Genton, M.G., and Guttorp, P. (2007), “Geostatistical Space-Time Models, Stationarity, Separability and Full Symmetry,” in Statistics of Spatio-Temporal Systems, eds. B. Finkenstaedt, L. Held, and V. Isham, Boca Raton: Chapman & Hall/CRC Press, pp. 151–175.
- Hutchinson, M.F. (1990), “A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines,” Communications in Statistics---Simulations, 19, 433–450.
- Jones, R.H., and Zhang, Y. (1997), “Models for Continuous Stationary Space-Time Processes,” in Modelling Longitudinal and Spatially Correlated Data, eds. T. G. Gregoire, D. R. Brillinger, P. J. Diggle, E. Russek-Cohen, W. G. Warren, and R. D. Wolfinger, New York: Springer, pp. 289–298.
- Kaufman, C., Schervish, M., and Nychka, D. (2008), “Covariance Tapering for Likelihood-Based Estimation in Large Spatial Datasets,” Journal of the American Statistical Association, 103, 1556–1569.
- Kitanidis, P.K. (1983), “Statistical Estimation of Polynomial Generalized Covariance Functions and Hydrologic Applications,” Water Resources Research, 19, 909–921.
- Kolotilina, L.Y., and Yeremin, A.Y. (1993), “Factorized Sparse Approximate Inverse Preconditioning I. Theory,” SIAM Journal on Matrix Analysis and Applications, 14, 45–58.
- Kozintsev, B. (1999), “Computations With Gaussian Random Fields,” Ph.D. dissertation, University of Maryland.
- Lindgren, F., Rue, H., and Lindström, J. (2011), “An Explicit Link Between Gaussian Fields and Gaussian Markov Random Fields: The SPDE Approach” (with discussion), Journal of the Royal Statistical Society, Series B, 73, 423–498.
- Olver, F. W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010), NIST Handbook of Mathematical Functions, New York, NY: Cambridge University Press.
- Rue, H., and Tjelmeland, H. (2002), “Fitting Gaussian Markov Random Fields to Gaussian Fields,” Scandinavian Journal of Statistics, 29, 31–50.
- Santner, T.J., Williams, B.J., and Notz, W.I. (2003), The Design and Analysis of Computer Experiments, New York: Springer.
- Stefanski, L.A., and Boos, D.D. (2002), “The Calculus of M-Estimation,” Journal of the American Statistical Association, 56, 29–38.
- Stein, M.L. (1999), Interpolation of Spatial Data: Some Theory for Kriging, New York: Springer.
- ——— (2013), “Statistical Properties of Covariance Tapers,” Journal of Computational and Graphical Statistics, 22, 866–885.
- Stein, M.L., Chen, J., and Anitescu, M. (2012), “Stochastic Approximation of Score Functions for Gaussian Processes,” Annals of Applied Statistics 7, 1162–1191.
- Stein, M.L., Chi, Z., and Welty, L.J. (2004), “Approximating Likelihoods for Large Spatial Datasets,” Journal of the Royal Statistical Society, Series B, 66, 275–296.
- Sun, Y., Li, B., and Genton, M.G. (2012), “Geostatistics for Large Datasets,” in Advances And Challenges In Space-Time Modelling Of Natural Events (Vol. 207, Chapter 3), eds. J. M. Montero, E. Porcu, M. Schlather, New York: Springer, pp. 55–77.
- Vecchia, A.V. (1988), “Estimation and Model Identification for Continuous Spatial Processes,” Journal of the Royal Statistical Society, Series B, 50, 297–312.
- Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
- Zhang, H. (2004), “Inconsistent Estimation and Asymptotically Equal Interpolations in Model Based Geostatistics,” Journal of the American Statistical Association, 99, 250–261.