Joint Composite Estimating Functions in Spatial and Spatio-Temporal Models.

Spatial or spatio-temporal data are frequently encountered in many scientific disciplines. One major challenge in modeling these processes is the high dimensionality of such data; that is, the number of observations is usually enormous. The first part of the dissertation proposes an efficient approach to analyzing spatio-temporal processes. We proposed a new method called joint composite estimating function (JCEF). It reduces the likelihood dimension by utilizing lower-dimensional marginal likelihoods in estimation and inference. This method allows us to account for high-order spatio-temporal dependences through Hansen's generalized method of moments. Simulation experiments show favorable improvement in estimation efficiency over the conventional composite likelihood methods when applied to estimating the spatio-temporal covariance functions. Large sample properties of the proposed JCEF estimator are derived under more realistic settings than what is available in the current literature.The second part of the thesis presents a much needed review of existing covariance estimation methods parallelly developed for massive spatial data sets. To thoroughly investigate their relative performances in spatio-temporal data analysis, we conduct extensive simulation experiments to compare estimation bias and efficiency among the most popularly used methods, including conventional pairwise composite likelihood, JCEF, Stein's conditional pseudo-likelihood, tapering, weighted least squares, and maximum likelihood, which is served as the golden standard.The third part of the thesis develops a new modeling and estimating framework for high-dimensional spatial-clustered data, termed as GeoCopula. Marginal distributions are assumed to be the generalized linear models, so that the new method can handle both discrete and continuous outcomes. The within-cluster and between-cluster spatial correlations are modeled by a multivariate Gaussian copula, which results in a fully parametric model for dependent data. This class of models generates population-level regression parameter estimates similar to GEE, while explicitly models the dependence structures separately from the mean model. Estimation and inference are achieved by applying the JCEF method. Through simulation experiments we show efficiency improvement over conventional pairwise composite likelihoods. The proposed model and method are illustrated by an analysis of the Gambia malaria data set.