Statistical Analysis of Spatial Data in the Presence of Missing Observations: A Methodological Guide and an Application to Urban Census Data

In this paper a simple introduction and guide to a widely applicable method for estimating missing data in fields of enquiry such as census maps or LANDSAT images are presented. The method given is a maximum likelihood procedure. This is argued to have the particularly favourable characteristics (1) that its distribution properties are known, (2) it is applicable both to regularly and to irregularly spaced observations, (3) it can handle different spatial configurations of missing cells, (4) it makes full use of the information contained in the known spatial data (particularly its spatial autocorrelation), (5) it has no systematic tendency to error, and (6) it provides ‘probability limits’. The algorithm is presented in the form of a simple tutorial guide. An example, of median income levels in Houston, is worked through in detail for missing cells in census data. The example is characterised by a variable mean and a general variance — covariance matrix.