A Study on Prediction Comparison of Kriging and Cokriging using PCA

Cokriging is a multivariate spatial method which estimates spatially correlated variables as an extension of kriging method in geostatistics. In the geostatistics, dataset structure of cokriging consists of locations and observed values for a sort of two variables (the primary variable and secondary variables) in the locations. The cokriging method is useful to predict the observe value for primary variable in an unknown location with the help of secondary variables. Generally, cokriging is conducted using one primary and one secondary variable. Because only one variable among secondary variables in this secondary dataset is used, information for secondary variables dataset is lost. Therefore, we propose the use of PCA interaction (PCAI : PCA with interaction among secondary variables) method to reduce two or more variables into one dimension as a secondary variable for cokriging technique. An actual numerical example is evaluated to prove the validity and usefulness of the proposed method using the air pollution (2015) data obtained from Korean statistical information service. In this paper, we compare Kriging, PCA and PCAI with the RMSE as criterion. The comparison result appeared that PCAI cokriging is superior to kriging and PCA cokriging respectively.