Cross-Covariance Functions for Multivariate Geostatistics

Marc G. Genton; William Kleiber

doi:10.1214/14-sts487

journal article May 01, 2015

Cross-Covariance Functions for Multivariate Geostatistics

Marc G. Genton William Kleiber

Statistical Science Vol. 30 No. 2 · Institute of Mathematical Statistics

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References

123

[1]

Calder, C. A. (2007). Dynamic factor process convolution models for multivariate space–time data with application to air quality assessment. Environ. Ecol. Stat. 14 229–247. 10.1007/s10651-007-0019-y

[2]

Gneiting, T. (2002). Nonseparable, stationary covariance functions for space–time data. J. Amer. Statist. Assoc. 97 590–600. 10.1198/016214502760047113

[3]

Furrer, R., Genton, M. G. and Nychka, D. (2006). Covariance tapering for interpolation of large spatial datasets. J. Comput. Graph. Statist. 15 502–523. 10.1198/106186006x132178

[4]

Gelfand, A. E., Banerjee, S. and Gamerman, D. (2005). Spatial process modelling for univariate and multivariate dynamic spatial data. Environmetrics 16 465–479. 10.1002/env.715

[5]

Kaufman, C. G., Schervish, M. J. and Nychka, D. W. (2008). Covariance tapering for likelihood-based estimation in large spatial data sets. J. Amer. Statist. Assoc. 103 1545–1555. 10.1198/016214508000000959

[6]

Berrocal, V. J., Gelfand, A. E. and Holland, D. M. (2010). A bivariate space–time downscaler under space and time misalignment. Ann. Appl. Stat. 4 1942–1975. 10.1214/10-aoas351

[7]

Apanasovich, T. V., Genton, M. G. and Sun, Y. (2012). A valid Matérn class of cross-covariance functions for multivariate random fields with any number of components. J. Amer. Statist. Assoc. 107 180–193. 10.1080/01621459.2011.643197

[8]

Fuentes, M. and Reich, B. (2013). Multivariate spatial nonparametric modelling via kernel processes mixing. Statist. Sinica 23 75–97. 10.5705/ss.2011.172

[9]

Gneiting, T., Kleiber, W. and Schlather, M. (2010). Matérn cross-covariance functions for multivariate random fields. J. Amer. Statist. Assoc. 105 1167–1177. 10.1198/jasa.2010.tm09420

[10]

Guhaniyogi, R., Finley, A. O., Banerjee, S. and Kobe, R. K. (2013). Modeling complex spatial dependencies: Low-rank spatially varying cross-covariances with application to soil nutrient data. J. Agric. Biol. Environ. Stat. 18 274–298. 10.1007/s13253-013-0140-3

[11]

Kleiber, W. and Genton, M. G. (2013). Spatially varying cross-correlation coefficients in the presence of nugget effects. Biometrika 100 213–220. 10.1093/biomet/ass057

[12]

Majumdar, A., Paul, D. and Bautista, D. (2010). A generalized convolution model for multivariate nonstationary spatial processes. Statist. Sinica 20 675–695.

[13]

Royle, J. A. and Berliner, L. M. (1999). A hierarchical approach to multivariate spatial modeling and prediction. J. Agric. Biol. Environ. Stat. 4 29–56. 10.2307/1400420

[14]

Sang, H., Jun, M. and Huang, J. Z. (2011). Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors. Ann. Appl. Stat. 5 2519–2548. 10.1214/11-aoas478

[15]

Gneiting, T. (2013). Strictly and non-strictly positive definite functions on spheres. Bernoulli 19 1327–1349. 10.3150/12-bejsp06

[16]

Mardia, K. V. and Goodall, C. R. (1993). Spatial–temporal analysis of multivariate environmental monitoring data. In Multivariate Environmental Statistics. North-Holland Ser. Statist. Probab. 6 347–386. North-Holland, Amsterdam.

[17]

Bornn, L., Shaddick, G. and Zidek, J. V. (2012). Modeling nonstationary processes through dimension expansion. J. Amer. Statist. Assoc. 107 281–289. 10.1080/01621459.2011.646919

[18]

Constantinescu, E. M. and Anitescu, M. (2013). Physics-based covariance models for Gaussian processes with multiple outputs. Int. J. Uncertain. Quantif. 3 47–71. 10.1615/int.j.uncertaintyquantification.2012003722

[19]

Fanshawe, T. R. and Diggle, P. J. (2012). Bivariate geostatistical modelling: A review and an application to spatial variation in Radon concentrations. Environ. Ecol. Stat. 19 139–160. 10.1007/s10651-011-0179-7

[20]

Castruccio, S. and Genton, M. G. (2014). Beyond axial symmetry: An improved class of models for global data. Stat 3 48–55. 10.1002/sta4.44

[21]

Jun, M. (2011). Non-stationary cross-covariance models for multivariate processes on a globe. Scand. J. Stat. 38 726–747. 10.1111/j.1467-9469.2011.00751.x

[22]

Jun, M. (2014). Matérn-based nonstationary cross-covariance models for global processes. J. Multivariate Anal. 128 134–146. 10.1016/j.jmva.2014.03.009

[23]

Kleiber, W., Katz, R. W. and Rajagopalan, B. (2013). Daily minimum and maximum temperature simulation over complex terrain. Ann. Appl. Stat. 7 588–612. 10.1214/12-aoas602

[24]

Calder, C. A. (2008). A dynamic process convolution approach to modeling ambient particulate matter concentrations. Environmetrics 19 39–48. 10.1002/env.852

[25]

Paciorek, C. J. and Schervish, M. J. (2006). Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 17 483–506. 10.1002/env.785

[26]

Gelfand, A. E., Schmidt, A. M., Banerjee, S. and Sirmans, C. F. (2004). Nonstationary multivariate process modeling through spatially varying coregionalization. TEST 13 263–312. 10.1007/bf02595775

[27]

Schlather, M. (2010). Some covariance models based on normal scale mixtures. Bernoulli 16 780–797. 10.3150/09-bej226

[28]

Sampson, P. D. and Guttorp, P. (1992). Nonparametric estimation of nonstationary spatial covariance structure. J. Amer. Statist. Assoc. 87 108–119. 10.1080/01621459.1992.10475181

[29]

Brown, P. J., Le, N. D. and Zidek, J. V. (1994). Multivariate spatial interpolation and exposure to air pollutants. Canad. J. Statist. 22 489–509. 10.2307/3315406

[30]

Fuentes, M. (2002). Spectral methods for nonstationary spatial processes. Biometrika 89 197–210. 10.1093/biomet/89.1.197

[31]

Daniels, M. J., Zhou, Z. and Zou, H. (2006). Conditionally specified space–time models for multivariate processes. J. Comput. Graph. Statist. 15 157–177. 10.1198/106186006x100434

[32]

Gelfand, A. E. and Vounatsou, P. (2003). Proper multivariate conditional autoregressive models for spatial data analysis. Biostatistics 4 11–25. 10.1093/biostatistics/4.1.11

[33]

Apanasovich, T. V. and Genton, M. G. (2010). Cross-covariance functions for multivariate random fields based on latent dimensions. Biometrika 97 15–30. 10.1093/biomet/asp078

[34]

Sain, S. R. and Cressie, N. (2007). A spatial model for multivariate lattice data. J. Econometrics 140 226–259. 10.1016/j.jeconom.2006.09.010

[35]

Majumdar, A. and Gelfand, A. E. (2007). Multivariate spatial modeling for geostatistical data using convolved covariance functions. Math. Geol. 39 225–245. 10.1007/s11004-006-9072-6

[36]

Ver Hoef, J. M., Cressie, N. and Barry, R. P. (2004). Flexible spatial models for kriging and cokriging using moving averages and the fast Fourier transform (FFT). J. Comput. Graph. Statist. 13 265–282. 10.1198/1061860043498

[37]

Kleiber, W. and Nychka, D. (2012). Nonstationary modeling for multivariate spatial processes. J. Multivariate Anal. 112 76–91. 10.1016/j.jmva.2012.05.011

[38]

Oehlert, G. W. (1993). Regional trends in sulfate wet deposition. J. Amer. Statist. Assoc. 88 390–399. 10.1080/01621459.1993.10476288

[39]

Gneiting, T. and Schlather, M. (2004). Stochastic models that separate fractal dimension and the Hurst effect. SIAM Rev. 46 269–282 (electronic). 10.1137/s0036144501394387

[40]

Cressie, N. A. C. (1993). Statistics for Spatial Data. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Wiley, New York. 10.1002/9781119115151

[41]

Interpolation of Spatial Data

Michael L. Stein

Springer Series in Statistics 10.1007/978-1-4612-1494-6

[42]

Bochner, S. (1955). Harmonic Analysis and the Theory of Probability. Univ. California Press, Berkeley and Los Angeles. 10.1525/9780520345294

[43]

Alonso-Malaver, C., Porcu, E. and Giraldo, R. (2013). Multivariate versions of walks through dimensions and Schoenberg measures. Technical report, Univ. Tecnica Federico Santa Maria, Valparaiso, Chile.

[44]

Bhat, K., Haran, M. and Goes, M. (2010). Computer model calibration with multivariate spatial output: A case study. In Frontiers of Statistical Decision Making and Bayesian Analysis (M.-H. Chen, D. K. Dey, P. Müller, D. Sun and K. Ye, eds.) 168–184. Springer, New York.

[45]

On the Theory of Stationary Random Processes

Harald Cramer

The Annals of Mathematics 10.2307/1968827

[46]

Daley, D. J., Porcu, E. and Bevilacqua, M. (2015). Classes of compactly supported correlation functions for multivariate random fields. Stoch. Environ. Risk Assess. To appear. 10.1007/s00477-014-0996-y

[47]

Gneiting, T., Genton, M. G. and Guttorp, P. (2007). Geostatistical space-time models, stationarity, separability and full symmetry. In Statistics of Spatio-Temporal Systems. Monographs in Statistics and Applied Probability (B. Finkenstaedt, L. Held and V. Isham, eds.) 151–175. Chapman & Hall/CRC Press, Boca Raton, FL. 10.1201/9781420011050.ch4

[48]

Guillot, G., Senoussi, R. and Monestiez, P. (2001). A positive definite estimator of the non stationary covariance of random fields. In GeoENV 2000: Third European Conference on Geostatistics for Environmental Applications (P. Monestiez, D. Allard and R. Froidevaux, eds.) 333–344. Kluwer Academic, Dordrecht. 10.1007/978-94-010-0810-5_29

[49]

Porcu, E., Bevilacqua, M. and Genton, M. G. (2014). Spatio-temporal covariance and cross-covariance functions of the great circle distance on a sphere. Unpublished manuscript.

[50]

Stein, M. L. (2005). Nonstationary spatial covariance functions. Technical Report 21, Univ. Chicago, CISES.

Showing 50 of 123 references

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Published: May 01, 2015
Vol/Issue: 30(2)

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Cite This Article

Marc G. Genton, William Kleiber (2015). Cross-Covariance Functions for Multivariate Geostatistics. Statistical Science, 30(2). https://doi.org/10.1214/14-sts487

Cross-Covariance Functions for Multivariate Geostatistics

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