  Despite of the great efforts during the censuses, occurrence of some
nonsampling errors such as coverage error is inevitable. Coverage error which
can be classified into two types of under-count and overcount occurs when there
is no unique bijective (one-to-one) mapping between the individuals from the
census count and the target population -- individuals who usually reside in the
country (de jure residences). There are variety of reasons make the coverage
error happens including deficiencies in the census maps, errors in the field
operations or disinclination of people for participation in the undercount
situation and multiple enumeration of individuals or those who do not belong to
the scope of the census in the overcount situation. A routine practice for
estimating the net coverage error is subtracting the census count from the
estimated true population, which obtained from a dual system (or
capture-recapture) technique. Estimated coverage error usually suffers from
significant uncertainty of the direct estimate of true population or other
errors such as matching error. To rectify the above-mentioned problem and
predict a more reliable coverage error rate, we propose a set of
spatio-temporal mixed models. In an illustrative study on the 2010 census
coverage error rate of the U.S. counties with population more than 100,000, we
select the best mixed model for prediction by deviance information criteria
(DIC) and conditional predictive ordinate (CPO). Our proposed approach for
predicting coverage error rate and its measure of uncertainty is a full
Bayesian approach, which leads to a reasonable improvement over the direct
coverage error rate in terms of mean squared error (MSE) and confidence
interval (CI) as provided by the U.S. Census Bureau.
