Joint composite estimating functions in spatiotemporal models

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2012-11, Vol.74 (5), p.799-824
• Main Authors: Bai, Yun, Song, Peter X.‐K, Raghunathan, T. E
• Format: Article
• Language: English
• Subjects: Asymptotic properties; Asymptotics; Bayesian method; Bayesian theory; Computation; Consistent estimators; Correlated data; Covariance; Covariance matrices; Data analysis; Dimension reduction; Economic models; Estimating; Estimating techniques; Estimation; Estimation methods; Estimators; Generalized method of moments; Mathematical analysis; Mathematical models; Maximum likelihood estimation; Modelling; particulates; probability analysis; Quadratic inference function; simulation models; Spacetime; Spatial analysis; Spatial data; spatial distribution; Standard error; Statistical analysis; Statistical methods; Statistical variance; Statistics; Studies; Temporal logic; temporal variation; U.S.A
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/j.1467-9868.2012.01035.x

Modelling of spatiotemporal processes has received considerable attention in recent statistical research. However, owing to the high dimensionality of the data, the joint modelling of spatial and temporal processes presents a great computational challenge, in both likelihood‐based and Bayesian approaches. We propose a joint composite estimating function approach to estimating spatiotemporal covariance structures. This substantially reduces the computational complexity and is more efficient than existing composite likelihood methods. The novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial, temporal and spatiotemporal cross‐pairs, which results in overidentified estimating functions. Thus, we form a joint inference function in a spirit that is similar to Hansen's generalized method of moments. We show that under practical scenarios the estimator proposed is consistent and asymptotically normal. Simulation studies prove that our method performs well in finite samples. Finally, we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates (PM10) in the north‐eastern USA over a 32‐month period.