Sandwich Estimation for Multi-Unit Reporting on a Stratified Heterogeneous Surface

Spatial sampling is widely used in environmental and social research. In this paper we consider the situation where instead of a single global estimate of the mean of an attribute for an area, estimates are required for each of many geographically defined reporting units (such as counties or grid cells) because their means cannot be assumed to be the same as the global figure. Not only may survey costs greatly increase if sample size has to be a function of the number of reporting units, estimator sampling error tends to be large if the population attribute of each reporting unit can be estimated by using only those samples actually lying inside the unit itself. This study proposes a computationally simple approach to multi-unit reporting by using analysis of variance and incorporating ‘twice-stratified’ statistics. We assume that, although the area is heterogeneous (the mean varies across the area), it can be zoned (or stratified) into homogeneous subareas (the mean is constant within each subarea) and, in addition, that it is possible to acquire prior knowledge about this partition. This zoning of the study area is independent of the reporting units. The zone estimates are transferred to the reporting units. We call the methodology sandwich estimation and we report two contrasting empirical studies to demonstrate the application of the methodology and to compare its performance against some other existing methods for tackling this problem. Our study shows that sandwich estimation performs well against two other frequently used, probabilistic, model-based approaches to multi-unit reporting on stratified heterogeneous surfaces whilst having the advantage of computational simplicity. We suggest those situations where sandwich estimation might be expected to do well.