Comparison between Matheron and Genton semivariance function estimators in spatial modeling of soybean yield

Abstract

In precision agriculture, interpolations are performed to map soybean yield, which facilitates decision making. Among the existing methods, geostatistics prevails, which uses information from the data’s spatial structure to generate interpolated maps. The spatial dependence structure is modeled based on the semivariogram, with the Matheron semivariance estimator being the most commonly used function. However, studies show unreliability in the presence of outliers; therefore, other researchers propose an alternative use of the Genton semivariance function estimator. Despite several studies comprising comparative works involving both estimators of the semivariance function, there are only a few comparative studies considering theoretical semivariograms with cyclical behavior, such as the Wave model. This study, therefore, aims to compare these two estimators considering adjustments of the Wave model in soybean yield data, when containing an outlier. The spatial dependence measure index was used to measure the degree of the model’s spatial dependence and the weighted Kappa index to assess the similarity of maps generated through kriging. It was possible to verify that the outlier removal was more impactful in the modeling considering the Matheron semivariance function estimator, thus confirming the robustness of the Genton semivariance function estimator