Generalized least‐squares in dimension expansion method for nonstationary processes

Abstract

AbstractIn this article, we consider the problem of modeling nonstationary spatial random processes. Bornn et al.(2012) proposed a dimension expansion method, a novel technique for modeling nonstationary processes, aiming to find a dimensionally sparse projection in which the originally nonstationary field exhibits stationarity. However, their dimension expansion approach is a lasso‐penalized least‐squares method that does not account for the covariance structure of the empirical semivariogram. We thus propose a general latent dimension estimation method by replacing the least‐squares method with generalized least‐squares (GLS). Furthermore, we improve the GLS method by weighted least‐squares, which is more computationally efficient and accurate. The performance of the proposed methods is demonstrated through simulations and real data examples.