Tapered Covariance: Bayesian Estimation and Asymptotics

References

• Banerjee, S., Gelfand, A.E., Finley, A.O., and Sang, H. (2008), “Gaussian Predictive Process Models for Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series B, 70, 825–848.
   Google Scholar
• Berger, J.O. (2000), “Bayesian Analysis: A Look at Today and Thoughts of Tomorrow,” Journal of the American Statistical Association, 95, 1269–1276.
   Web of Science ®Google Scholar
• Bhapkar, V.P. (1972), “On a Measure of Efficiency of an Estimating Equation,” Sankhyā, Series A, 34, 467–472.
   Google Scholar
• Chernozhukov, V., and Hong, H. (2003), “An MCMC Approach to Classical Estimation,” Journal of Econometrics, 115, 293–346.
   Web of Science ®Google Scholar
• Cressie, N. A.C. (1991), Statistics for Spatial Data, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, New York: Wiley.
   Google Scholar
• Cressie, N., and Johannesson, G. (2008), “Fixed Rank Kriging for Very Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series B, 70, 209–226.
   Google Scholar
• Curriero, F.C., and Lele, S. (1999), “A Composite Likelihood Approach to Semivariogram Estimation,” Journal of Agricultural, Biological, and Environmental Statistics, 4, 9–28.
   Web of Science ®Google Scholar
• Du, J., Zhang, H., and Mandrekar, V. (2009), “Fixed-Domain Asymptotic Properties of Tapered Maximum Likelihood Estimators,” The Annals of Statistics, 37, 3330–3361.
   Web of Science ®Google Scholar
• Durbin, J. (1960), “Estimation of Parameters in Time-Series Regression Models,” Journal of the Royal Statistical Society, Series B, 22, 139–153.
   Google Scholar
• Ferreira, P.E. (1982), “Multiparametric Estimating Equations,” Annals of the Institute of Statistical Mathematics, 34, 423–431.
   Web of Science ®Google Scholar
• Finley, A., Sang, H., Banerjee, S., and Gelfand, A. (2009), “Improving the Performance of Predictive Process Modeling for Large Datasets,” Computational Statistics & Data Analysis, 53, 2873–2884.
   PubMed Web of Science ®Google Scholar
• Fuentes, M. (2007), “Approximate Likelihood for Large Irregularly Spaced Spatial Data,” Journal of the American Statistical Association, 102, 321–331.
   PubMed Web of Science ®Google Scholar
• Furrer, R., and Bengtsson, T. (2007), “Estimation of High-Dimensional Prior and Posterior Covariance Matrices in Kalman Filter Variants,” Journal of Multivariate Analysis, 98, 227–255.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Furrer, R., and Sain, S. (2009), “Spatial Model Fitting for Large Datasets With Applications to Climate and Microarray Problems,” Statistics and Computing, 19, 113–128.
   Web of Science ®Google Scholar
• Godambe, V.P., and Heyde, C.C. (1987), “Quasi-Likelihood and Optimal Estimation,” International Statistical Review, 55, 231–244.
   Web of Science ®Google Scholar
• Heagerty, P.J., and Lele, S.R. (1998), “A Composite Likelihood Approach to Binary Spatial Data,” Journal of the American Statistical Association, 93, 1099–1111.
   Web of Science ®Google Scholar
• Heyde, C.C. (1997), Quasi-Likelihood and Its Application: A General Approach to Optimal Parameter Estimation, Springer Series in Statistics, New York: Springer-Verlag.
   Google Scholar
• Horn, R.A., and Johnson, C.R. (1991), Topics in Matrix Analysis, Cambridge: Cambridge University Press.
   Google Scholar
• Kauermann, G., and Carroll, R.J. (2001), “A Note on the Efficiency of Sandwich Covariance Matrix Estimation,” Journal of the American Statistical Association, 96, 1387–1396.
   Web of Science ®Google Scholar
• Kaufman, C. (2006), “Covariance Tapering for Likelihood-Based Estimation in Large Spatial Datasets,” Ph.D. dissertation, Carnegie Mellon University, Pittsburgh, PA.
   Google Scholar
• 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, 1545–1569.
   Web of Science ®Google Scholar
• Mardia, K.V., and Marshall, R.J. (1984), “Maximum Likelihood Estimation of Models for Residual Covariance in Spatial Regression,” Biometrika, 71, 135–146.
   Web of Science ®Google Scholar
• Matsuda, Y., and Yajima, Y. (2009), “Fourier Analysis of Irregularly Spaced Data on Rd,” Journal of the Royal Statistical Society, Series B, 71, 191–217.
   Google Scholar
• Morton, R. (1981), “Efficiency of Estimating Equations and the Use of Pivots,” Biometrika, 68, 227–233.
   Web of Science ®Google Scholar
• Stein, M.L. (1999), Interpolation of Spatial Data: Some Theory for Kriging, Springer Series in Statistics, New York: Springer-Verlag.
   Google Scholar
• Stein, M.L., Chi, Z., and Welty, L.J. (2004), “Approximating Likelihoods for Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series B, 66, 275–296.
   Google Scholar
• Vecchia, A.V. (1988), “Estimation and Model Identification for Continuous Spatial Processes,” Journal of the Royal Statistical Society, Series B, 50, 297–312.
   Google Scholar
• Wendland, H. (1995), “Piecewise Polynomial, Positive Definite and Compactly Supported Radial Functions of Minimal Degree,” Advances in Computational Mathematics, 4, 389–396.
   Google Scholar
• ——— (1998), “Error Estimates for Interpolation by Compactly Supported Radial Basis Functions of Minimal Degree,” Journal of Approximation Theory, 93, 258–272.
   Web of Science ®Google Scholar
• Whittle, P. (1954), “On Stationary Processes in the Plane,” Biometrika, 41, 434–449.
   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.
   Web of Science ®Google Scholar
• Zhang, H., and Du, J. (2008), “Covariance Tapering in Spatial Statistics,” in Positive Definite Functions: From Schoenberg to Space-Time Challenges, eds. J. Mateu and E. Porcu, Spain: Gráficas Casta n, s.l.
   Google Scholar
• Zhang, H., and Zimmerman, D.L. (2005), “Towards Reconciling Two Asymptotic Frameworks in Spatial Statistics,” Biometrika, 92, 921–936.
   Web of Science ®Google Scholar
• Zimmerman, D.L. (1989), “Computationally Exploitable Structure of Covariance Matrices and Generalized Covariance Matrices in Spatial Models,” Journal of Statistical Computation and Simulation, 32, 1–15.
   Google Scholar