Restricted maximum likelihood (REML) estimation in empirical Bayes smoothing of census undercount - ARCHIVED

One way to assess the undercount at subnational levels (e.g. the state level) is to obtain sample data from a post-enumeration survey, and then smooth those data based on a linear model of explanatory variables. The relative importance of sampling-error variances to corresponding model-error variances determines the amount of smoothing. Maximum likelihood estimation can lead to oversmoothing, so making the assessment of undercount over-reliant on the linear model. Restricted maximum likelihood (REML) estimators do not suffer from this drawback. Empirical Bayes prediction of undercount based on REML will be presented in this article, and will be compared to maximum likelihood and a method of moments by both simulation and example. Large-sample distributional properties of the REML estimators allow accurate mean squared prediction errors of the REML-based smoothers to be computed.