Estimation and smoothing from incomplete data for a class of lattice processes

Abstract

Multidimensional discrete-parameter processes with factorable covariance structure are of great importance for applications and approximations to certain continuous parameter processes. In practical situations, usually only incomplete data are available, so state-space schemes are normally used for modelling and prediction. In this work we describe maximum-likelihood estimation and smoothing for doubly geometric lattice processes using incomplete data. The procedure proposed is based on an application of the EM algorithm, and is inspired by its use in time-series analysis. Minimum mean-square-error prediction is also described. Extension to more general models is commented on. Some examples using simulated data are provided.

Keywords:

• Lattice processes
• incomplete data
• EM algorithm
• maximum likelihood
• smoothing
• prediction