Cressie N
J Am Stat Assoc. 1989 Dec;84(408):1,033-44.
Empirical Bayes methods are used to estimate the extent of the undercount at the local level in the 1980 U.S. census. "Grouping of like subareas from areas such as states, counties, and so on into strata is a useful way of reducing the variance of undercount estimators. By modeling the subareas within a stratum to have a common mean and variances inversely proportional to their census counts, and by taking into account sampling of the areas (e.g., by dual-system estimation), empirical Bayes estimators that compromise between the (weighted) stratum average and the sample value can be constructed. The amount of compromise is shown to depend on the relative importance of stratum variance to sampling variance. These estimators are evaluated at the state level (51 states, including Washington, D.C.) and stratified on race/ethnicity (3 strata) using data from the 1980 postenumeration survey (PEP 3-8, for the noninstitutional population)."
经验贝叶斯方法用于估计1980年美国人口普查中地方层面漏报的程度。“将州、县等区域内相似的子区域分组形成层，是减少漏报估计量方差的一种有效方法。通过对子区域进行建模，使其在一个层内具有共同均值且方差与人口普查计数成反比，并考虑区域抽样（例如，通过双系统估计），可以构建在（加权）层均值和样本值之间进行折中的经验贝叶斯估计量。结果表明，折中的程度取决于层方差与抽样方差的相对重要性。使用1980年事后调查（针对非机构人口的PEP 3 - 8）的数据，在州层面（51个州，包括华盛顿特区）对这些估计量进行评估，并按种族/族裔进行分层（3个层）。”
