Coverage Technical Report, Census of Population, 2016
9. Estimation
Estimation for the DCS, the RRC and the COS is covered in Section 6.2, Section 7.4 and Section 8.5, respectively. This section describes how the results of census coverage studies are combined to produce estimates of population undercoverage ($U$), population overcoverage ($O$) and population net undercoverage ($N$) in different domains. The impact of sampling errors on the quality of the estimates is also measured by an estimated standard error for each estimate. Reverse Record Check (RRC) results and census data are used to produce undercoverage estimates, while the Census Overcoverage Survey (COS) results estimate overcoverage. Net undercoverage is the difference between undercoverage and overcoverage. This section expands on how these estimates and the associated standard errors are calculated.
The following definitions are used:
$\widehat{U}$ is calculated using RRC results and census data, and $\widehat{O}$ is produced from the COS, as shown below:
Components^{Table 9.1 Note 1}  Number of persons 

Estimate of U  1,557,061 
Estimate of O  707,335 
Estimate of N  849,726 
C  35,151,728 
C + estimate of N  36,001,454 

The estimated standard errors are defined as follows:
By definition, we have $v(\widehat{U})=v\left(\widehat{M}\right)$ (refer to Section 7.4.7).
Therefore:
$se(\widehat{U})=\sqrt[]{v(\widehat{M})}$
$se\left({\widehat{R}}_{U}\right)=\sqrt{\left(\frac{{\widehat{U}}^{2}+{\widehat{T}}^{2}2\widehat{U}\widehat{T}}{{\widehat{T}}^{4}}\right)v\left(\widehat{M}\right)+\frac{{\widehat{U}}^{2}}{{\widehat{T}}^{4}}v\left(\widehat{O}\right)}$
$se\left(\widehat{O}\right)=\sqrt[]{v(\widehat{O})}$
$se\left({\widehat{R}}_{O}\right)=\sqrt{\left(\frac{{\widehat{O}}^{2}}{{\widehat{T}}^{4}}\right)v(\widehat{M})+\left(\frac{{\widehat{U}}^{2}+{\widehat{T}}^{2}2\widehat{O}\widehat{T}}{{\widehat{T}}^{4}}\right)v(\widehat{O})}$
$se\left(\widehat{N}\right)=\sqrt[]{v(\widehat{M})+v(\widehat{O})}$
$se\left({\widehat{R}}_{N}\right)=\sqrt{\left(\frac{{(\widehat{U}\widehat{O})}^{2}+{\widehat{T}}^{2}2(\widehat{U}\widehat{O}){\widehat{T}}^{2}}{{\widehat{T}}^{4}}\right)\left[v(\widehat{M})+v(\widehat{O})\right]}$
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