LarocqueDutilleulPelletierEtAl2007

Référence

Larocque, G., Dutilleul, P., Pelletier, B. and Fyles, J.W. (2007) Characterization and quantification of uncertainty in coregionalization analysis. Mathematical Geology, 39(3):263-288. (Scopus )

Résumé

Coregionalization analysis has been presented as a method of multi-scale analysis for multivariate spatial data. Despite an increasing use of this method in environmental and earth sciences, the uncertainty associated with the estimation of parameters in coregionalization analysis (e.g., sills and functions of sills) is potentially high and has not yet been characterized. This article aims to discuss the theory underlying coregionalization analysis and assess the robustness and limits of the method. A theoretical framework is developed to calculate the ergodic and fluctuation variance-covariance matrices of least-squares estimators of sills in the linear model of coregionalization. To adjust for the positive semidefiniteness constraint on estimated coregionalization matrices, a confidence interval estimation procedure for sills and functions of sills is presented. Thereafter, the relative importance of uncertainty measures (bias and variance) for sills and structural coefficients of correlation and determination is assessed under different scenarios to identify factors controlling their uncertainty. Our results show that the sampling grid density, the choice of the least-squares estimator of sills, the positive semidefiniteness constraint, the presence of scale dependence in the correlations, and the number and range of variogram models, all affect the level of uncertainty, sometimes through multiple interactions. The asymptotic properties of variogram model parameter estimators in a bounded sampling domain impose a theoretical limit to their accuracy and precision. Because of this limit, the uncertainty was found to be high for several scenarios, especially with three variogram models, and was often more dependent on the ratio of variogram range to domain extent than on the sampling grid density. In practice, in the coregionalization analysis of a real dataset, the circular requirement for sill estimates in the calculation of uncertainty measures makes the quantification of uncertainty very problematic, if not impossible. The use of coregionalization analysis must be made with due knowledge of the uncertainty levels and limits of the method. © International Association for Mathematical Geology 2007.

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@ARTICLE { LarocqueDutilleulPelletierEtAl2007,
    AUTHOR = { Larocque, G. and Dutilleul, P. and Pelletier, B. and Fyles, J.W. },
    TITLE = { Characterization and quantification of uncertainty in coregionalization analysis },
    JOURNAL = { Mathematical Geology },
    YEAR = { 2007 },
    VOLUME = { 39 },
    PAGES = { 263-288 },
    NUMBER = { 3 },
    ABSTRACT = { Coregionalization analysis has been presented as a method of multi-scale analysis for multivariate spatial data. Despite an increasing use of this method in environmental and earth sciences, the uncertainty associated with the estimation of parameters in coregionalization analysis (e.g., sills and functions of sills) is potentially high and has not yet been characterized. This article aims to discuss the theory underlying coregionalization analysis and assess the robustness and limits of the method. A theoretical framework is developed to calculate the ergodic and fluctuation variance-covariance matrices of least-squares estimators of sills in the linear model of coregionalization. To adjust for the positive semidefiniteness constraint on estimated coregionalization matrices, a confidence interval estimation procedure for sills and functions of sills is presented. Thereafter, the relative importance of uncertainty measures (bias and variance) for sills and structural coefficients of correlation and determination is assessed under different scenarios to identify factors controlling their uncertainty. Our results show that the sampling grid density, the choice of the least-squares estimator of sills, the positive semidefiniteness constraint, the presence of scale dependence in the correlations, and the number and range of variogram models, all affect the level of uncertainty, sometimes through multiple interactions. The asymptotic properties of variogram model parameter estimators in a bounded sampling domain impose a theoretical limit to their accuracy and precision. Because of this limit, the uncertainty was found to be high for several scenarios, especially with three variogram models, and was often more dependent on the ratio of variogram range to domain extent than on the sampling grid density. In practice, in the coregionalization analysis of a real dataset, the circular requirement for sill estimates in the calculation of uncertainty measures makes the quantification of uncertainty very problematic, if not impossible. The use of coregionalization analysis must be made with due knowledge of the uncertainty levels and limits of the method. © International Association for Mathematical Geology 2007. },
    ADDRESS = { Department of Plant Science, McGill University, Macdonald Campus, Ste-Anne-de-Bellevue, QC H9X 3V9, Canada },
    COMMENT = { Export Date: 24 August 2007 Source: Scopus doi: 10.1007/s11004-007-9086-8 Language of Original Document: English Correspondence Address: Larocque, G.; Department of Natural Resource Sciences; McGill University; Macdonald Campus Ste-Anne-de-Bellevue, QC H9X 3V9, Canada; email: guillaume.larocque@mcgill.ca },
    ISSN = { 08828121 (ISSN) },
    KEYWORDS = { Direct and cross variograms, Ergodic, estimation and fluctuation variances, Least-squares estimators of sills, Multi-scale analysis, Positive semidefiniteness, Structural correlations and coefficients of determination },
    OWNER = { brugerolles },
    TIMESTAMP = { 2007.12.05 },
    URL = { http://www.scopus.com/scopus/inward/record.url?eid=2-s2.0-34447344041&partnerID=40&rel=R6.5.0 },
}

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