Estimating deformations of isotropic Gaussian random fields on the plane

Annals of Statistics

Volumn 36, Issue 2, 2008, Pages 719-741

  Anderes, Ethan B ^a   Stein, Michael L ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Deformation; Nonstationary random fields; Quasiconformal maps

Indexed keywords

EID: 51049107702     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000893     Document Type: Article

References (21)

1. AHLFORS, L. V. (1966). Lectures on Quasiconformal Mappings. Van Nostrand, Toronto. MR0200442
2. ANDERES, E. B. and STEIN, M. L. (2005). Estimating deformations of isotropic gaussian random fields on the plane. Technical report, Center for Integrating Statistical and Environmental Science. Available at http://galton.uchicago.edu/~cises/rescarch/cises-tr27.pdf.
3. CHILÈS, J. and DELFINER, P. (1999). Geostatistics: Modeling Spatial Uncertainty. Wiley, New York. MR1679557
4. CLERC, M. and MALLAT. S. (2002). The texture gradient equation for recovering shape from texture. IEEE Trans. Pattern Analysis and Machine Intelligence 24 536-549.
5. CLERC, M. and MALLAT, S. (2003). Estimating deformations of stationary processes. Ann. Statist. 31 1772-1821. MR2036390
6. CRESSIE, N. (1993). Statistics for Spatial Data, rev. ed. Wiley, New York. MR1239641
7. DAMIÁN, D., SAMPSON, P. and GUTTORP, P. (2001). Bayesian estimation of semi-parametric non-stationary spatial covariance structures. Environmetrics 12 161-178.
8. GARDINER, F. P. and LAKIC, N. (2000). Quasiconformal Teichmüller Theory. Amer. Math. Soc., Providence, RI. MR 1730906
9. GOLUB, G. H. and VAN LOAN, C. F. (1996). Matrix Computations. Johns Hopkins Univ. Press. MR1417720
10. GIJYON, X. and PERRIN. O. (2000). Identification of space deformation using linear and superficial quadratic variations. Statist. Probab. Lett. 47 307-316. MR1747492
11. IOVLEFF, S. and PERRIN, O. (2004). Estimating a nonstationary spatial structure using simulated annealing. J. Comput. Graph. Statist. 13 90-105. MR2044872
12. KRANTZ, S. G. (2004). Complex Analysis: The Geometric Viewpoint, 2nd ed. Mathematical Association of America. Washington, DC. MR2047863
13. KRUSHKAL', S. L. (1979). Quasiconformal Mappings and Riemann Surfaces. Winston. Washington. DC. MR0536488
14. LAWRYNOWICZ. J. (1983). Quasiconformal Mappings in the Plane: Parametrical Methods. Springer, Berlin. MR0702025
15. LEHTO, O. and VIRTANEN, K. I. (1965). Quasiconformal Mappings in the Plane. Springer, New York. MR0344463
16. PERRIN, O. and MEIRING, W. (1999). Identifiability for nonstationary spatial structure. J. Appl. Probab. 36 1244-1250. MR1746409
17. RABINER, L. and JUANG, B. (1993). Fundamentals of Speech Recognition. Prentice-Hall, Englewood Cliffs, NJ.
18. SAMPSON. P. and GUTTORP, P. (1992). Nonparametric estimation of nonstationary spatial covariance structure. J. Amer. Statist. Assoc.87108-119.
19. SCHMIDT, A. and O'HAGAN, A. (2003). Bayesian inference for nonstationary spatial covariance structure via spatial deformations. J. Roy. Statist. Soc. Ser. B 65 745-758. MR1998632
20. SILVERMAN, R. A. (1974). Complex Analysis with Applications. Prentice-Hall, Englewood Cliffs, NJ. MR0352421
21. STEIN, M. L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. Springer, New York. MR1697409