Nonstationary modeling for multivariate spatial processes

Journal of Multivariate Analysis

Volumn 112, Issue , 2012, Pages 76-91

  Kleiber, William ^a   Nychka, Douglas ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Cross covariance; Kernel smoother; Local stationarity; Mat rn; Multivariate; Nonstationary; Spatial Gaussian process

Indexed keywords

EID: 84863476484     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2012.05.011     Document Type: Article

References (46)

1. Altman N.S. Kernel smoothing of data with correlated errors. Journal of the American Statistical Association 1998, 85:749-759.
2. Anderes E.B., Stein M.L. Local likelihood estimation for nonstationary random fields. Journal of Multivariate Analysis 2011, 102:506-520.
3. Apanasovich T.V., Genton M.G. Cross-covariance functions for multivariate random fields based on latent dimensions. Biometrika 2010, 97:15-30.
4. Apanasovich T.V., Genton M.G., Sun Y. A valid Matérn class of cross-covariance functions for multivariate random fields with any number of components. Journal of the American Statistical Association 2012, 107:180-193.
5. Bhatia R. Positive Definite Matrices 2007, Princeton Press.
6. Boyd S., Xiao L. Least-squares covariance matrix adjustment. SIAM Journal on Matrix Analysis and Applications 2005, 27:532-546.
7. Fan J. Design-adaptive nonparametric regression. Journal of the American Statistical Association 1992, 87:998-1004.
8. Fuentes M. Spectral methods for nonstationary spatial processes. Biometrika 2002, 89:197-210.
9. Gaspari G., Cohn S.E. Construction of correlation functions in two and three dimensions. Quarterly Journal of the Royal Meteorological Society 1999, 125:723-757.
10. Gelfand A.E., Schmidt A.M., Banerjee S., Sirmans C.F. Nonstationary multivariate process modeling through spatially varying coregionalization (with discussion and rejoinder). Test 2004, 13:263-312.
11. Genton M.G. Separable approximations of space-time covariance matrices. Environmetrics 2007, 18:681-695.
12. Gneiting T., Kleiber W., Schlather M. Matérn cross-covariance functions for multivariate random fields. Journal of the American Statistical Association 2010, 105:1167-1177.
13. T. Gneiting, H. Ševčíková, D.B. Percival, Estimators of fractal dimension: assessing the roughness of time series and spatial data, 2011, [stat.ME]. arxiv:1101.1444v1.
14. Goulard M., Voltz M. Linear coregionalization model: tools for estimation and choice of cross-variogram matrix. Mathematical Geology 1992, 24:269-282.
15. Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series, and Products 2000, Academic Press, London. sixth ed.
16. Guillot G., Senoussi R., Monestiez P. A positive definite estimator of the nonstationary covariance of random fields. GeoENV 2000: Third European Conference on Geostatistics for Environmental Applications 2001, 333-344. Kluwer Academic, Dordrecht, The Netherlands. P. Monestiez, D. Allard, R. Froidevaux (Eds.).
17. Guttorp P., Gneiting T. Studies in the history of probability and statistics XLIX: on the Matérn correlation family. Biometrika 2006, 93:989-995.
18. Hart J.D., Wehrly T.E. Kernel regression estimation using repeated measurements data. Journal of the American Statistical Association 1986, 81:1080-1088.
19. Higdon D. A process-convolution approach to modelling temperatures in the North Atlantic Ocean. Environmental and Ecological Statistics 1998, 5:173-190.
20. Higham N.J. Computing the nearest correlation matrix-a problem from finance. IMA Journal of Numerical Analysis 2002, 22:329-343.
21. Jun M. Nonstationary cross-covariance models for multivariate processes on a globe. Scandinavian Journal of Statistics 2011, 38:726-747.
22. Jun S., Knutti R., Nychka D.W. Spatial analysis to quantify numerical model bias and dependence: how many climate models are there?. Journal of the American Statistical Association 2008, 103:934-947.
23. Jun M., Szunyogh I., Genton M.G., Zhang F., Bishop C.H. A statistical investigation of the sensitivity of ensemble-based Kalman filters to covariance filtering. Monthly Weather Review 2011, 139:3036-3051.
24. Li B., Zhang H. An approach to modeling asymmetric multivariate spatial covariance structures. Journal of Multivariate Analysis 2011, 102:1445-1453.
25. Lindgren F., Rue H., Lindström J. An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society (Series B) 2011, 73:423-498.
26. Majumdar A., Gelfand A.E. Multivariate spatial modeling for geostatistical data using convolved covariance functions. Mathematical Geology 2007, 39:225-245.
27. Majumdar A., Paul D., Bautista D. A generalized convolution model for multivariate nonstationary spatial processes. Statistica Sinica 2010, 20:675-695.
28. Mardia K., Goodall C. Spatial-temporal analysis of multivariate environmental monitoring data. Multivariate Environmental Statistics 1993, 347-386. North Holland, Amsterdam. G.P. Patil, C.R. Rao (Eds.).
29. Mearns L.O., Gutowski W.J., Jones R., Leung L., McGinnis A.M., Nunes B., Qian Y. A regional climate change assessment program for North America. Eos, Transactions, American Geophysical Union 2009, 90:311-312.
30. North G.R., Wang J., Genton M.G. Correlation models for temperature fields. Journal of Climate 2011, 24:5850-5862.
31. Oehlert G.W. Regional trends in sulfate wet deposition. Journal of the American Statistical Association 1993, 88:390-399.
32. C. Paciorek, Nonstationary Gaussian processes for regression and spatial modelling, Ph.D. Thesis, Carnegie Mellon University, Department of Statistics, 2003.
33. Paciorek C.J., Schervish M.J. Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 2006, 17:483-506.
34. Porcu E., Mateu J., Christakos G. Quasi-arithmetic means of covariance functions with potential applications to space-time data. Journal of Multivariate Analysis 2009, 100:1830-1844.
35. Porcu E., Zastavnyi V. Characterization theorems for some classes of covariance functions associated to vector valued random fields. Journal of Multivariate Analysis 2011, 102:1293-1301.
36. Sain S.R., Furrer R., Cressie N. A spatial analysis of multivariate output from regional climate models. Annals of Applied Statistics 2011, 5:150-175.
37. Sampson P.D., Guttorp P. Nonparametric estimation of nonstationary spatial covariance structure. Journal of the American Statistical Association 1992, 87:108-119.
38. Schlather M. Some covariance models based on normal scale mixtures. Bernoulli 2010, 16:780-797.
39. Smith R.L., Tebaldi C., Nychka D., Mearns L.O. Bayesian modeling of uncertainty in ensembles of climate models. Journal of the American Statistical Association 2009, 104:97-116.
40. Stein M.L. Interpolation of Spatial Data: Some Theory for Kriging 1999, Springer-Verlag, New York.
41. M.L. Stein, Nonstationary spatial covariance functions, University of Chicago, CISES Technical Report 21, 2005.
42. Tebaldi C., Mearns L., Nychka D., Smith R. Regional probabilities of precipitation change: a Bayesian analysis of multimodel simulations. Geophysical Research Letters 2004, 31.
43. Tebaldi C., Sansó B. Joint projections of temperature and precipitation change from multiple climate models: a hierarchical Bayesian approach. Journal of the Royal Statistical Society (Series A) 2009, 172:83-106.
44. Ver Hoef J.M., Barry R.P. Constructing and fitting models for cokriging and multivariable spatial prediction. Journal of Statistical Planning and Inference 1998, 69:275-294.
45. Wackernagel H. Multivariate Geostatistics 2003, Springer-Verlag, Berlin. third ed.
46. Wand M.P., Jones M.C. Kernel Smoothing 1995, Chapman and Hall.