Effects of Confidentiality-Preserving Geo-Masking on the Estimation of Semivariogram and of the Kriging Variance

Geostatistical methods, such as semivariograms and kriging are well-known spatial tools commonly employed in many disciplines such as health, mining, forestry, meteorology to name only few. They are based essentially on point-referenced data on a continuous space and on the calculation of distances between them. In many practical instances, however, the exact point location, even if exactly known, is geo-masked to preserve confidentiality. This typically happens when dealing with confidential data related to individuals-health and their biometric parameters. In these situations, the estimation of the semivariogram and, hence, the spatial prediction can become biased and highly inefficient. This paper examines the extent of the bias in the particular case when the geo-masking mechanism is known (called “intentional locational error”) and lays the ground to a full understanding of the phenomenon in more general cases. We also examine how the geo-masking affects the estimation of the kriging variance thus reducing the efficiency of spatial prediction. We pursue our aims by developing some theoretical results and by making use of simulated and real data analysis.