Small Area Condence Bounds on Small Cell Proportions in Survey Populations

Motivated by the problems of ‘quality ltering’ of estimated counts in American Community Survey (ACS) tables, and of reporting small-domain coverage results from the Census Coverage Measurement (CCM) program, this paper studies methods for placing condence bounds on proportions for cells and tables, estimated from complex surveys, in which the estimated counts are zeroes. While coecients of variation are generally used in measuring the quality of estimated counts, they do not make sense for assessing validity of very small estimated counts. The problem is formulated here in terms of (upper) condence bounds for unknown proportions. We discuss methods of creating condence bounds from small-area models including logistic, beta-binomial, and variance-stabilized (arcsin square root transformed) linear models. The model-based condence bounds are compared with single-cell bounds derived from arcsin-square-root transformed binomial intervals with survey weights embodied in the ‘eective sample size’. The comparison is illustrated on county-level data about Housing-Unit Erroneous Enumeration status from the 2010 CCM.