Modified linear projection for large spatial datasets

Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial datasets. These sorts of datasets can be found in various fields of the natural and social sciences. However, model fitting and spatial prediction using these large spatial datasets are impractically time-consuming, because of the necessary matrix inversions. Various methods have been developed to deal with this problem, including a reduced rank approach and a sparse matrix approximation. In this article, we propose a modification to an existing reduced rank approach to capture both the large- and small-scale spatial variations effectively. We have used simulated examples and an empirical data analysis to demonstrate that our proposed approach consistently performs well when compared with other methods. In particular, the performance of our new method does not depend on the dependence properties of the spatial covariance functions.