Groupe d’études et de recherche en analyse des décisions

Composite Joint Estimating Functions and Applications in Spatio-Temporal Models

Peter X.K. Song

Modeling of spatio-temporal processes has received considerable attention in recent statistical research. However, due to high dimensionality of the data, joint modeling of the spatial and temporal processes presents great computational challenge in both likelihood-based and Bayesian approaches. In this talk, I will present a composite joint estimating function (CJEF) approach to estimating spatio-temporal covariance structures, which substantially reduces the dimensionality and computational complexity and is more efficient than existing composite likelihood methods in spatial/temporal applications. The novelty of the proposed CJEF lies in the construction of three sets of estimating functions from spatial, temporal and cross pairs respectively. To deal with the issue that the resulting set of estimating functions contains more equations than the number of parameters, we form a quadratic inference function in a similar spirit to Hansen's generalized method of moments for estimation. We show that the proposed method yields consistent estimation and the estimator is asymptotically normal under practical scenarios. Simulations prove that our method performs very well in finite samples. Finally, we apply our method to study the spatio-temporal dependence structure of PM10 particles in northeastern United States. This is the joint work with Yun Bai and T.E. Raghunathan.