Nonstationary Positive Definite Tapering On The Plane

REFERENCES

• Ahlfors , L. 2006 . Lectures on Quasiconformal Mappings: University Lecture Series 38 (with additional chapters by , Edited by: Earle , C. J. , Kra , I. , Shishikura , M. and Hubbard , J.H. Providence , RI : Amer. Math. Soc .
   Google Scholar
• Anderes , E. and Chatterjee , S. 2009 . “Consistent Estimates of Deformed Isotropic Gaussian Random Fields on the Plane,” . The Annals of Statistics , 37 : 2324 – 2350 .
   Google Scholar
• Anderes , E. and Coram , M. 2011 . “Two Dimensional Density Estimation Using Smooth Invertible Transformations,” . Journal of Statistical Planning and Inference , 141 : 1183 – 1193 .
   Google Scholar
• Anderes , E. and Stein , M. 2008 . “Estimating Deformations of Isotropic Gaussian Random Fields on the Plane,” . The Annals of Statistics , 36 : 719 – 741 .
   Web of Science ®Google Scholar
• Clerc , M. and Mallat , S. 2002 . “Estimating Deformations of Stationary Processes,” . The Annals of Statistics , 31 : 1772 – 1821 .
   Google Scholar
• Cressie , N. 1990 . “The Origins of Kriging,” . Mathematical Geology , 22 : 239 – 252 .
   Google Scholar
• Damian , C. , Sampson , P. and Guttorp , P. 2001 . “Bayesian Estimation of Semi-Parametric Non-Stationary Spatial Covariance Structures,” . Environmetrics , 12 : 161 – 178 .
   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
• Furrer , R. , Genton , M. 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
• Iovleff , S. and Perrin , O. 2004 . “Estimating a Nonstationary Spatial Structure Using Simulated Annealing,” . Journal of Computational and Graphical Statistics , 13 : 90 – 105 .
   Web of Science ®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 – 1555 .
   Web of Science ®Google Scholar
• Matheron , G. 1963 . “Principles of Geostatistics,” . Economic Geology , 58 : 1246 – 1266 .
   Google Scholar
• McCann , R. 1995 . “Existence and Uniqueness of Monotone Measure-Preserving Maps,” . Duke Mathematical Journal , 80 : 309 – 323 .
   Web of Science ®Google Scholar
• Perrin , O. and Meiring , W. 1999 . “Identifiability for Non-Stationary Spatial Structure,” . Journal of Applied Probability , 36 : 1244 – 1250 .
   Web of Science ®Google Scholar
• Sampson , P. and Guttorp , P. 1992 . “Nonparametric Estimation of Nonstationary Spatial Covariance Structure,” . Journal of the American Statistical Association , 87 : 108 – 119 .
   Web of Science ®Google Scholar
• Schmidt , A. and O’Hagan , A. 2003 . “Bayesian Inference for Nonstationary Spatial Covariance Structure via Spatial Deformations,” . Journal of the Royal Statistical Society, Series B , 65 : 745 – 758 .
   Google Scholar
• Shaby , B. and Ruppert , D. 2012 . “Tapered Covariance: Bayesian Estimation and Asymptotics,” . Journal of Computational and Graphical Statistics , 21 : 433 – 452 .
   Web of Science ®Google Scholar
• Stein , M. 1999 . Interpolation of Spatial Data: Some Theory for Kriging , New York : Springer .
   Google Scholar
• Wahba , G. 1990 . Spline Models for Observational Data , Philadelphia , PA : SIAM .
   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
• Zhang , H. and Du , J. 2008 . “Covariance Tapering in Spatial Statistics,” . In Positive Definite Functions: From Schoenberg to Space-Time Challenges , Edited by: Mateu , J. and Porcu , E. 181 – 196 . Castelló , , de la Plana, Spain : University Jaume I .
   Google Scholar