Assessing the significance of the correlation between the components of a bivariate Gaussian random field
Assessing the significance of the correlation between the components of a bivariate random field is of great interest in the analysis of spatial data. This problem has been addressed in the literature using suitable hypothesis testing procedures or using coefficients of spatial association between t...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2015
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/9009
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/9009
- Palabra clave:
- Cross-covariance estimation
Geostatistics
Hypothesis testing
Increasing domain
Power function
Arsenic
Assessment method
Autocorrelation
Estimation method
Geostatistics
Hypothesis testing
Lead
Numerical method
Numerical model
Power law
Spatial data
Testing method
United States
Utah
- Rights
- restrictedAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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Assessing the significance of the correlation between the components of a bivariate Gaussian random field |
| title |
Assessing the significance of the correlation between the components of a bivariate Gaussian random field |
| spellingShingle |
Assessing the significance of the correlation between the components of a bivariate Gaussian random field Cross-covariance estimation Geostatistics Hypothesis testing Increasing domain Power function Arsenic Assessment method Autocorrelation Estimation method Geostatistics Hypothesis testing Lead Numerical method Numerical model Power law Spatial data Testing method United States Utah |
| title_short |
Assessing the significance of the correlation between the components of a bivariate Gaussian random field |
| title_full |
Assessing the significance of the correlation between the components of a bivariate Gaussian random field |
| title_fullStr |
Assessing the significance of the correlation between the components of a bivariate Gaussian random field |
| title_full_unstemmed |
Assessing the significance of the correlation between the components of a bivariate Gaussian random field |
| title_sort |
Assessing the significance of the correlation between the components of a bivariate Gaussian random field |
| dc.subject.keywords.none.fl_str_mv |
Cross-covariance estimation Geostatistics Hypothesis testing Increasing domain Power function Arsenic Assessment method Autocorrelation Estimation method Geostatistics Hypothesis testing Lead Numerical method Numerical model Power law Spatial data Testing method United States Utah |
| topic |
Cross-covariance estimation Geostatistics Hypothesis testing Increasing domain Power function Arsenic Assessment method Autocorrelation Estimation method Geostatistics Hypothesis testing Lead Numerical method Numerical model Power law Spatial data Testing method United States Utah |
| description |
Assessing the significance of the correlation between the components of a bivariate random field is of great interest in the analysis of spatial data. This problem has been addressed in the literature using suitable hypothesis testing procedures or using coefficients of spatial association between two sequences. In this paper, testing the association between autocorrelated variables is addressed for the components of a bivariate Gaussian random field using the asymptotic distribution of the maximum likelihood estimator of a specific parametric class of bivariate covariance models. Explicit expressions for the Fisher information matrix are given for a separable and a nonseparable version of the parametric class, leading to an asymptotic test. The empirical evidence supports our proposal, and as a result, in most of the cases, the new test performs better than the modified t test even when the bivariate covariance model is misspecified or the distribution of the bivariate random field is not Gaussian. Finally, to illustrate how the proposed test works in practice, we study a real dataset concerning the relationship between arsenic and lead from a contaminated area in Utah, USA. © 2015 John Wiley & Sons, Ltd. |
| publishDate |
2015 |
| dc.date.issued.none.fl_str_mv |
2015 |
| dc.date.accessioned.none.fl_str_mv |
2020-03-26T16:32:45Z |
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2020-03-26T16:32:45Z |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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Artículo |
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publishedVersion |
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Environmetrics; Vol. 26, Núm. 8; pp. 545-556 |
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11804009 |
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https://hdl.handle.net/20.500.12585/9009 |
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10.1002/env.2367 |
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Universidad Tecnológica de Bolívar |
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Repositorio UTB |
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7102698888 7005667849 54783771000 |
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Environmetrics; Vol. 26, Núm. 8; pp. 545-556 11804009 10.1002/env.2367 Universidad Tecnológica de Bolívar Repositorio UTB 7102698888 7005667849 54783771000 |
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https://hdl.handle.net/20.500.12585/9009 |
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eng |
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eng |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/restrictedAccess |
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Atribución-NoComercial 4.0 Internacional |
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Recurso electrónico |
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application/pdf |
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John Wiley and Sons Ltd |
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John Wiley and Sons Ltd |
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2020-03-26T16:32:45Z2020-03-26T16:32:45Z2015Environmetrics; Vol. 26, Núm. 8; pp. 545-55611804009https://hdl.handle.net/20.500.12585/900910.1002/env.2367Universidad Tecnológica de BolívarRepositorio UTB7102698888700566784954783771000Assessing the significance of the correlation between the components of a bivariate random field is of great interest in the analysis of spatial data. This problem has been addressed in the literature using suitable hypothesis testing procedures or using coefficients of spatial association between two sequences. In this paper, testing the association between autocorrelated variables is addressed for the components of a bivariate Gaussian random field using the asymptotic distribution of the maximum likelihood estimator of a specific parametric class of bivariate covariance models. Explicit expressions for the Fisher information matrix are given for a separable and a nonseparable version of the parametric class, leading to an asymptotic test. The empirical evidence supports our proposal, and as a result, in most of the cases, the new test performs better than the modified t test even when the bivariate covariance model is misspecified or the distribution of the bivariate random field is not Gaussian. Finally, to illustrate how the proposed test works in practice, we study a real dataset concerning the relationship between arsenic and lead from a contaminated area in Utah, USA. © 2015 John Wiley & Sons, Ltd.Recurso electrónicoapplication/pdfengJohn Wiley and Sons Ltdhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_16echttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84955210414&doi=10.1002%2fenv.2367&partnerID=40&md5=cd0225a6b14777a4d734a5644a43e02dAssessing the significance of the correlation between the components of a bivariate Gaussian random fieldinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Cross-covariance estimationGeostatisticsHypothesis testingIncreasing domainPower functionArsenicAssessment methodAutocorrelationEstimation methodGeostatisticsHypothesis testingLeadNumerical methodNumerical modelPower lawSpatial dataTesting methodUnited StatesUtahBevilacqua M.Vallejos R.Velandia D.Apanasovich, T., Genton, M.G., Cross-covariance functions for multivariate random fields based on latent dimensions (2010) Biometrika, 97, pp. 15-30Apanasovich, T., Genton, M.G., Sun, Y., A valid Matérn class of cross-covariance functions for multivariate random fields with any number of components (2012) Journal of the American Statistical Association, 107, pp. 180-193Bevilacqua, M., Hering, A.S., Porcu, E., On the flexibility of multivariate covariance models: comment on the paper by Genton and Kleiber (2015) Statistical Science, 30 (2), pp. 167-169Bevilacqua, M., Gaetan, C., Comparing composite likelihood methods based on pairs for spatial Gaussian random fields (2015) Statistics and Computing, 25, pp. 877-982Blanco-Moreno, H.M., Chamorro, C., Sanz, F.X., Spatial and temporal patterns of lolium rigidum-avena sterilis mixed populations in a cereal field (2006) European Weed Research Society Weed Research, 46, pp. 207-218Chen, H.S., Simpson, D.G., Ying, Z., Fixed-domain asymptotics for a stochastic process model with measurement error (2000) Statistica Sinica, 10, pp. 141-156Clifford, P., Richardson, S., Hémon, D., Assessing the significance of the correlation between two spatial processes (1989) Biometrics, 45, pp. 123-134Córdoba, M., Bruno, C., Costa, J., Balzarini, M., Subfield management class delineation using cluster analysis from spatial principal components of soil variables (2013) Computers and Electronics Agriculture, 97, pp. 6-14Cuevas, F., Porcu, E., Vallejos, R., Study of spatial relationships between two sets of variables: a nonparametric approach (2013) Journal of Nonparametric Statistics, 25, pp. 695-714Daley, D.J., Porcu, E., Bevilacqua, M., Classes of compactly supported covariance functions for multivariate random fields (2015) Stochastic Environmental Research and Risk Assessment, 29, pp. 1249-1263Dutilleul, P., Modifying the t test for assessing the correlation between two spatial processes (1993) Biometrics, 49, pp. 305-314Genton, M.G., Kleiber, W., Cross-covariance functions for multivariate geostatistics (2015) Statistical Science, 3, pp. 147-163Gneiting, T., Kleiber, W., Schlather, M., Matérn cross-covariance functions for multivariate random fields (2010) Journal of the American Statistical Association, 105, pp. 1167-1177Griffith, D., The geographic distribution of soil-lead concentration: description and concerns (2002) URISA Journal, 14, pp. 5-15Griffith, D., Paelinck, J.H.P., (2011) Non-Standard Spatial Statistics, , Springer: New YorkGoovaerts, P., (1997) Geostatistics for Natural Resources Evaluation, , Oxford University Press: OxfordHaining, R., Bivariate correlation with spatial data (1991) Geographical Analysis, 23, pp. 210-227Lee, S., Developing a bivariate spatial association measure: an integration of Pearson's r and Moran's I (2001) Journal of Geographical Systems, 3, pp. 369-385Loh, W.L., Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields (2005) The Annals of Statistics, 33, pp. 2344-2394Ma, C., Covariance matrix functions of vector chi-square random fields in space and time (2011) IEEE Transactions on Communications, 59, pp. 2554-2561Ma, C., Student's t Vector random fields with power-law and log-law decaying direct and cross covariances (2013) Stochastic Analysis and Applications, 31, pp. 167-182Mardia, K.V., Marshall, R.J., Maximum likelihood estimation of models for residual covariance in spatial regression (1984) Biometrika, 71, pp. 135-146Matheron, G., (1965) Les Variables Régionalisées et leur Estimation, , Masson: ParisOjeda, S., Vallejos, R., Lamberti, P., Measure of similarity between images based on the codispersion coefficient (2012) Journal of Electronic Imaging, 21Osorio, F., Vallejos, R., (2014), http://cran.r-project.org/web/packages/SpatialPack/, SpatialPack: A package to assess the association between two spatial processes. R package version 0.2-3Padoan, S., Bevilacqua, M., Analysis of random fields using CompRandFld (2015) Journal of Statistical Software, 63, pp. 1-27Porcu, E., Daley, D.J., Buhmann, M.D., Bevilacqua, M., Radial basis functions with compact support for multivariate geostatistics (2013) Stochastic Environmental Research and Risk Assessment, 27, pp. 909-922Pringle, M.J., Lark, R.M., Spatial analysis of model error, illustrated by soil carbon dioxide emissions (2006) Vadose Zone Journal, 5, pp. 168-183Rukhin, A., Vallejos, R., Codispersion coefficient for spatial and temporal series (2008) Statistics and Probability Letters, 78, pp. 1290-1300Tjøstheim, D., A measure of association for spatial variables (1978) Biometrika, 65, pp. 109-114Vallejos, R., Assessing the association between two spatial or temporal sequences (2008) Journal of Applied Statistics, 35, pp. 1323-1343Vallejos, R., Testing for the absence of correlation between two spatial or temporal sequences (2012) Pattern Recognition Letters, 33, pp. 1741-1748Vallejos, R., Mallea, A., Herrera, M., Ojeda, S.M., A multivariate geostatistical approach for landscape classification from remotely sensed image data (2015) Stochastic Environmental Research and Risk Assessment, 29, pp. 365-369Varin, C., Reid, N., Firth, D., An overview of composite likelihood methods (2011) Statistica Sinica, 21, pp. 5-42Viladomat, J., Mazumder, R., McInturff, A., McCauley, D.J., Hastie, T., Assessing the significance of global and local correlations under spatial autocorrelation: a nonparametric approach (2014) Biometrics, 70, pp. 409-418Wackernagel, H., (2003) Multivariate Geostatictics. An Introduction with Applications, , 3rd Edition. Springer - Verlag: Berlin HeidelbergWendland, H., Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree (1995) Advances in Computational Mathematics, 4, pp. 389-396Zhang, H., Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics (2004) Journal of the American Statistical Association, 99, pp. 250-261Zhang, H., Maximum-likelihood estimation for multivariate spatial linear coregionalization models (2007) Environmetrics, 18, pp. 125-139Zhang, H., El-Shaarawi, A., On spatial skew-Gaussian processes and applications (2010) Environmetrics, 21, pp. 33-47http://purl.org/coar/resource_type/c_6501THUMBNAILMiniProdInv.pngMiniProdInv.pngimage/png23941https://repositorio.utb.edu.co/bitstream/20.500.12585/9009/1/MiniProdInv.png0cb0f101a8d16897fb46fc914d3d7043MD5120.500.12585/9009oai:repositorio.utb.edu.co:20.500.12585/90092021-02-02 14:22:10.383Repositorio Institucional UTBrepositorioutb@utb.edu.co |