Statistical Matching Analysis for Complex Survey Data With Applications

The goal of statistical matching is the estimation of a joint distribution having observed only samples from its marginals. The lack of joint observations on the variables of interest is the reason of uncertainty about the joint population distribution function. In the present article, the notion of matching error is introduced, and upper-bounded via an appropriate measure of uncertainty. Then, an estimate of the distribution function for the variables not jointly observed is constructed on the basis of a modification of the conditional independence assumption in the presence of logical constraints. The corresponding measure of uncertainty is estimated via sample data. Finally, a simulation study is performed, and an application to a real case is provided. Supplementary materials for this article are available online.

统计匹配（statistical matching）的目标是在仅观测到某联合分布的边缘分布样本的前提下，对该联合分布进行估计。由于缺乏针对所关注变量的联合观测数据，联合总体分布函数的估计存在不确定性。本文首先引入匹配误差（matching error）的概念，并通过恰当的不确定性测度推导其上界；随后，在存在逻辑约束的场景下，对条件独立性假设进行修正，并基于此构建未联合观测变量的分布函数估计量。对应的不确定性测度可通过样本数据进行估计。最后，本文开展了模拟研究，并给出了一则实际案例应用。本文的补充材料可在线获取。