A Statistical Approach to the Problem of Missing Spatial Data Using a First-Order Markov Model

Geographical data sets sometimes contain missing observations that need to be estimated. A statistical approach to the problem is discussed for multivariate normal spatial data sets satisfying the first-order spatial Markov property with constant mean, where the information at neighboring or contiguous observed sites is used to estimate the missing values. The completed data are used to estimate the parameters of the distribution. The procedure is iterative. The approach is a special case of the Orchard and Woodbury missing information principle. The paper concludes with an illustrative empirical example using rainfall data from an area of Kansas and Nebraska. The quality of the estimates for different sites are compared.