Intizar Muhammad Nadeem, Shehzad Muhammad Ahmed, Khurram Haris, Iftikhar Soofia, Khan Aamna, Kashif Abdul Rauf
Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Pattani, Thailand.
Heliyon. 2024 Jul 4;10(13):e33969. doi: 10.1016/j.heliyon.2024.e33969. eCollection 2024 Jul 15.
The endogeneity problem arises when the auxiliary variables correlate to the error terms. In such cases, appropriate instrumental variables ensure efficient estimation. Calibration has recognized itself as an important methodological tool at a large scale to estimate the population total in survey sampling. Which does not offer efficient estimation in the presence of endogeneity. When endogeneity is present in the auxiliary variables, the calibration using endogenous auxiliary variables may produce biasedness and increase variance due to inappropriate model assumptions. In this article, we propose instrumental-variable calibrated estimators by using the classical instrumental-variables approach for the case of exact identification that are more efficient than conventional calibration estimators when some auxiliary variables are endogenous. The necessary properties of the proposed estimators are presented. Our study is backed by both the simulation study and a real data example to check the performance of the proposed estimators.
当辅助变量与误差项相关时，就会出现内生性问题。在这种情况下，合适的工具变量可确保有效估计。校准已成为大规模调查抽样中估计总体总量的重要方法工具。但在校正存在时，它并不能提供有效估计。当辅助变量存在内生性时，使用内生辅助变量进行校准可能会由于不适当的模型假设而产生偏差并增加方差。在本文中，我们针对恰好识别的情况，使用经典工具变量方法提出了工具变量校准估计量，当一些辅助变量存在内生性时，这些估计量比传统校准估计量更有效。文中给出了所提估计量的必要性质。我们的研究得到了模拟研究和一个实际数据示例的支持，以检验所提估计量的性能。
