Nonresponse is a common problem in survey sampling. Appropriate treatment can be challenging, especially when dealing with detailed breakdowns of totals. Often, the nearest neighbour imputation method is used to handle such incomplete multinomial data. In this article, we investigate the nearest neighbour ratio imputation (NNRI) estimator, in which auxiliary variables are used to identify the closest donor and the vector of proportions from the donor is applied to the total of the recipient to implement ratio imputation. To estimate the asymptotic variance, we first treat the NNRI as a special case of predictive matching imputation and build on earlier work to linearize the imputed estimate. To account for the non-negligible sampling fractions, parametric and generalized additive models are employed to incorporate the smoothness of the imputation estimator, which results in a valid variance estimator. We apply the proposed method to estimate expenditures detail items based on empirical data from the 2018 collection of the Service Annual Survey, conducted by the United States Census Bureau. Our simulation results demonstrate the validity of our proposed estimators and also confirm that the derived variance estimators have good performance even when the sampling fraction is non-negligible.

中文翻译：

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调查抽样中不完整多项结果的最近邻比插补


无答复是调查抽样中的一个常见问题。适当的处理可能具有挑战性，尤其是在处理总数的详细分类时。通常，最近邻插补方法用于处理此类不完整的多项数据。在本文中，我们研究了最近邻比率插补（NNRI）估计器，其中辅助变量用于识别最近的捐赠者，并将捐赠者的比例向量应用于接受者的总数以实现比率插补。为了估计渐近方差，我们首先将 NNRI 视为预测匹配插补的特例，并在早期工作的基础上对插补估计进行线性化。为了考虑不可忽略的采样分数，采用参数和广义加性模型来合并插补估计器的平滑度，从而产生有效的方差估计器。我们根据美国人口普查局进行的 2018 年服务年度调查收集的经验数据，应用所提出的方法来估算支出明细项目。我们的模拟结果证明了我们提出的估计量的有效性，并且还证实了即使采样分数不可忽略，导出的方差估计量也具有良好的性能。