Tests of Significance for Structural Correlations in the Linear Model of Coregionalization

In the linear model of coregionalization (LMC), when applicable to the experimental direct variograms and the experimental cross variogram computed for two random functions, the variability of and relationships between the random functions are modeled with the same basis functions. In particular, structural correlations can be defined from entries of sill matrices (coregionalization matrices) under second-order stationarity. In this article, modified t-tests are proposed for assessing the statistical significance of estimated structural correlations. Their specific aspects and fundamental differences, compared with an existing modified t-test for global correlation analysis with spatial data, are discussed via estimated effective sample sizes, in relation to the superimposition of random structural components, the range of autocorrelation, the presence of correlation at another structure, and the sampling scheme. Accordingly, simulation results are presented for one structure versus two structures (one without and the other with autocorrelation). The performance of tests is shown to be related to the uncertainty associated with the estimation of variogram model parameters (range, sill matrix entries), because these are involved in the test statistic and the degrees of freedom of the associated t-distribution through the estimated effective sample size. Under the second-order stationarity and LMC assumptions, the proposed tests are generally valid.