In a finite population sampling survey, auxiliary information is commonly used to improve the Horvitz–Thompson estimators and calibration has been extensively used by national statistical agencies over the last decades for that purpose. This method enables to make estimators consistent with known totals of auxiliary variables and to reduce variance if the calibration variables are explanatory for the variable of interest. Nowadays, it is not unusual anymore to have high-dimensional auxiliary data sets and adding too much additional calibration variables may increase the variance of calibration estimators. We study in this paper the asymptotic efficiency of the calibration estimator with high-dimensional auxiliary data sets and we prove that it may suffer from an additional variability that may not be neglected in certain conditions. We suggest a bootstrap criterion in the choice of calibration variables. A short simulation study shows that the proposed method may lead to a more parsimonious number of calibration variables with associated weights of smaller variation and no variance inflation.

在有限人口抽样调查中，辅助信息通常用于改进 Horvitz-Thompson 估计量，而校准在过去几十年中已被国家统计机构广泛用于此目的。如果校准变量对感兴趣的变量具有解释性，则该方法能够使估计量与已知的辅助变量总数保持一致并减少方差。如今，拥有高维辅助数据集并添加过多额外校准变量可能会增加校准估计量的方差已不再罕见。我们在本文中研究了具有高维辅助数据集的校准估计器的渐近效率，我们证明它可能会受到在某些条件下可能不会被忽略的额外可变性的影响。我们建议在选择校准变量时采用引导标准。一个简短的模拟研究表明，所提出的方法可能会导致校准变量的数量更少，相关的权重变化更小，并且没有方差膨胀。