Robust estimation of correlation coefficients among soil parameters under the multivariate normal framework

• Robustness of correlation estimates under the multivariate normal framework is investigated.
• The well known method based on the Pearson moment-product correlation is the least robust.
• The methods based on the Spearman and Kendall rank correlations are more robust.
• The method based on the CDF transform is robust as long as the CDF is properly chosen.

Based on limited amount of multivariate soil data Y, it is only possible to reliably estimate the marginal distributions and the correlations. A common practical approach of constructing the multivariate probability distribution of Y is to transform Y into standard normal data X and construct the multivariate standard normal distribution for X. This method is called the translation method. Its success depends on whether the Pearson product-moment correlations (δij) for X can be robustly estimated. This paper investigates the robustness for four methods of estimating δij. The emphasis is on the statistical uncertainty in the estimated δij when the amount of soil data is limited. It is found that the well known method that maps the Pearson correlations for Y to δij is the least robust, suffering the most significant statistical uncertainty. The causes for this non-robustness are investigated. The two methods that map the Spearman and Kendall rank correlations for Y to δij are quite robust. The method that converts Y to X and directly estimates δij is also robust as long as the conversion is based on properly chosen marginal distributions.