When two surveys carried out separately in the same population have common variables, it might be desirable to adjust each survey’s weights so that they give equal estimates for the common variables. This problem has been studied extensively and has often been referred to as ‘alignment’ or ‘numerical consistency’. We develop a design-based empirical likelihood approach for alignment and estimation of complex parameters defined by estimating equations. We focus on a general case when a single set of adjusted weights, which can be applied to both common and non-common variables, is produced for each survey. The main contribution of the paper is to show that the empirical log-likelihood ratio statistic is pivotal in presence of alignment constraints. This pivotal statistic can be used to test hypotheses and derive confidence regions. Hence, the empirical likelihood approach proposed for alignment possesses the self-normalization property, under a design-based approach. The proposed approach accommodates large sampling fractions, stratification and population level auxiliary information. It is particularly well suited for inference about small domains, when data are skewed. It includes implicit adjustments when the samples considerably differ in size. The confidence regions are constructed without the need for variance estimates, joint-inclusion probabilities, linearisation and re-sampling.

中文翻译：

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对齐来自多项调查的信息的经验似然法

当在同一人口中分别进行的两项调查具有共同变量时，可能需要调整每个调查的权重，以便它们对共同变量给出相等的估计值。这个问题已被广泛研究，通常被称为“对齐”或“数值一致性”。我们开发了一种基于设计的经验似然方法，用于对齐和估计由估计方程定义的复杂参数。我们关注一个一般情况，即为每个调查生成一组调整后的权重，可以应用于共同和非共同变量。该论文的主要贡献是表明经验对数似然比统计量在存在对齐约束的情况下至关重要。此关键统计量可用于检验假设并推导出置信区域。因此，在基于设计的方法下，为对齐提出的经验似然方法具有自归一化特性。所提出的方法适应大的抽样分数、分层和总体水平辅助信息。当数据倾斜时，它特别适用于对小域的推断。当样本大小差异很大时，它包括隐式调整。置信区域的构建不需要方差估计、联合包含概率、线性化和重新采样。当数据倾斜时，它特别适用于对小域的推断。当样本大小差异很大时，它包括隐式调整。置信区域的构建不需要方差估计、联合包含概率、线性化和重新采样。当数据倾斜时，它特别适用于对小域的推断。当样本大小差异很大时，它包括隐式调整。置信区域的构建不需要方差估计、联合包含概率、线性化和重新采样。