Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets

Various approximation methods have been developed to address the computational difficulties. In this paper, we propose new unbiased estimating equations based on score equation approximations that are both computationally and statistically efficient.

We replace the inverse covariance matrix that appears in the score equations by a sparse matrix to approximate the quadratic forms, then set the resulting quadratic forms equal to their expected values to obtain unbiased estimating equations. The sparse matrix is constructed by a sparse inverse Cholesky approach to approximate the inverse covariance matrix. The statistical efficiency of the resulting unbiased estimating equations are evaluated both in theory and by numerical studies.