Abstract: The generalized estimating equations (GEE) method is a popular approach for analyzing dependent data of various types. While GEE estimators are robust against the misspecification of the correlation matrix, their estimation efficiency can be seriously affected by the choice of the working correlation matrix. For spatially correlated data, it is difficult to specify the true spatial correlation structure due to the complexity of dependence and the high dimension of spatial correlation matrices. To achieve estimation efficiency while allowing flexibility to capture complex spatial dependence, we propose a new GEE-type approach based on a mixture of spatial working correlation matrices, referred to as mix-GEE. We show that the mix-GEE estimator is asymptotically efficient without any parametric assumption on the distribution as long as one of the candidate correlation structures or some linear combination is correctly specified. Moreover, to overcome challenges in obtaining the inverse of the high-dimensional spatial correlation matrix for the large data set, we develop a tapered mix-GEE algorithm to reduce the computational cost and guarantee the estimation efficiency when the spatial correlation can be captured by the mixture correlation structure. The advantages of the proposed methods are demonstrated through simulations and the analysis of soil chemistry data.

Key words and phrases: Estimation efficiency, generalized estimating equations, misspecification, spatial data.