Empirical best prediction (EBP) is a well-known method for producing reliable proportion estimates when the primary data source provides only small or no sample from finite populations. There are at least two potential challenges encountered in implementing the existing EBP methodology. First, one must accurately link the sample to the finite population frame. This may be a difficult or even impossible task because of absence of identifiers that can be used to link sample and the frame. Secondly, the finite population frame typically contains limited auxiliary variables, which may not be adequate for building a reasonable working predictive model. We propose a data linkage approach in which we replace the finite population frame by a big sample that does not have the outcome binary variable of interest, but has a large set of auxiliary variables. Our proposed method calls for fitting the assumed model using data from the smaller sample, imputing the outcome variable for all the units of the big sample, and then finally using these imputed values to obtain standard weighted proportion using the big sample. We develop a new adjusted maximum likelihood method to avoid estimates of model variance on the boundary encountered in the commonly used in maximum likelihood estimation method. We propose an estimator of mean squared prediction error (MSPE) using a parametric bootstrap method and address computational issues by developing efficient EM algorithm. We illustrate the proposed methodology in the context of election projection for small areas.

翻译：经验最佳预测（EBP）是一种在主要数据源仅提供有限或无样本来自有限总体时，用于生成可靠比例估计的知名方法。实施现有EBP方法至少面临两个潜在挑战。首先，必须准确地将样本与有限总体框架相关联。由于缺乏可用于关联样本与框架的标识符，这可能是一项困难甚至不可能完成的任务。其次，有限总体框架通常包含有限的辅助变量，可能不足以构建合理的工作预测模型。我们提出一种数据关联方法，其中用一个不包含感兴趣二值结果变量但拥有大量辅助变量的大样本来替代有限总体框架。我们提出的方法要求使用较小样本的数据拟合假定模型，对所有大样本单元的结果变量进行插补，然后利用这些插补值通过大样本获得标准加权比例。我们开发了一种新的调整最大似然方法，以避免在常用的最大似然估计方法中遇到的模型方差估计位于边界上的问题。我们提出了一种使用参数自助法估计均方预测误差（MSPE）的方法，并通过开发高效的期望最大化（EM）算法解决计算问题。我们以选举预测为背景，针对小区域展示了所提出的方法的应用。