Application of em-type algorithms to spatial data

Abstract

We consider the problem of maximum-likelihood estimation and smoothing for lattice processes using incomplete data. In a previous paper (Alonso et al. 1996) the authors developed a methodology based on an application of the EM algorithm on a state-space framework for this problem. Now, the procedure is extended using new versions of EM-type algorithms (ECM and MCECM). This has computational advantages, especially when there are many parameters to estimate. The problem of estimating the asymptotic covariance matrix for the parameter estimators is also considered (supplemented EM-type algorithms). The steps are described through an application considering the underlying state model to have an AR(l)xAR(l) structure and extension to more general models is commented on. As an example, we apply the method to the data presented by Kempton and Howes (1981).

Keywords:

• Ecm algorithm
• em algorithm
• incomplete data
• lattice processe
• maximum likelihood
• mcecm algorithm
• prediction
• secm algorithm
• smoothing