Estimating the Count Error in the Australian Census

Abstract

In many countries, counts of people are a key factor in the allocation of government resources. However, it is well known that errors arise in Census counting of people (e.g., undercoverage due to missing people). Therefore, it is common for national statistical agencies to conduct one or more “audit” surveys that are designed to estimate and remove systematic errors in Census counting. For example, the Australian Bureau of Statistics (ABS) conducts a single audit sample, called the Post Enumeration Survey (PES), shortly after each Australian Population Census. This article describes the estimator used by the ABS to estimate the count of people in Australia. Key features of this estimator are that it is unbiased when there is systematic measurement error in Census counting and when nonresponse to the PES is nonignorable.

The framework for estimating coverage in the 2011 Census of England and Wales: Combining dual-system estimation with ratio estimation

“…Following the results in Eqs (16) to (18) we can move up to the level of the hard-to-count stratum h within an estimation area e E Ŷ eha |Y pa , X pa…”

“…Further adjustments to the definition ofw pa incorporate directly an adjustment for over-count when estimating the total population. Full details are given in [17,18].…”

“…The simulation results in Section 3 demonstrate that the framework for estimation proposed in Section 2, building on the 2001 approach [38], has good properties with respect to both bias and variability when combining cluster level dual-system estimation, Eqs (16)- (18), with simple ratio estimation. However, to implement the framework for the 2011 Census, several additional issues needed to be dealt with.…”

“…In particular, the US Census Bureau has a long history of assessing census coverage using a survey, dating back to the 1950 Census [8], although the alternative estimates produced in [9] show that estimating census coverage has always been difficult. Starting with analysis post 1980 [10,11], followed by developments at subsequent censuses, the Bureau's primary approach is now based on dual-system estimation [12] with a large national post-enumeration survey [13][14][15][16] Australian Bureau of Statistics also developed an estimation approach to combine its census with a survey during the 1980s and the current implementation for 2011 is developed and discussed in [17,18]. Other examples include the approach used for the 2000 Census of Switzerland, as outlined in [19], and for Israel, as outlined in [20].…”

On the Estimation of Population Size from a Dependent Triple-Record System

“…However, in some instances, duplicate records or members outside the target population are included in the census or any other registers because of erroneous enumeration. This issue is known as overcoverage, and it is a common practice to identify and remove the erroneous inclusions through administrative follow-up actions (Chipperfield et al, 2017) or to adjust the census data on the basis of an estimate of the overcoverage rate (Zhang, 2015). In this paper, we focus only on the issues that are related to the commonly encountered problem of undercoverage, assuming that the available data are free from any erroneous inclusion.…”