Abstract
Dual-system estimation is a well-established approach for estimating an unknown population size from two independent but imperfect counts of the population. In this paper we develop the estimation framework for using a coverage survey and population census as the two sources and combining with ratio estimation to produce a set of population estimates. Adjustments are developed to correct for a failure of the key assumptions of homogeneity and independence that under-pin dual-system estimation using an external count of the number of households. The issue of over-count within the census is also discussed and a bootstrap approach to variance estimation is proposed. A comprehensive set of simulation results are presented to support the decision to implement the framework to estimate the population following the 2011 Census of England and Wales; and the implementation to the estimation of census coverage in 2011 is discussed.
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