The Nested Error Regression Model with High-Dimensional Parameters (NERHDP) is extended to address challenges in small area poverty estimation. A robust and flexible framework is proposed to derive empirical best predictors (EBPs) of small area poverty indicators while accommodating heterogeneity in regression coefficients and sampling variances across areas. To mitigate the computational limitations of the existing algorithm, an efficient estimation procedure is introduced, substantially reducing computation time and enhancing scalability for large datasets. A novel approach for generating area-specific poverty estimates in out-of-sample areas is also developed, improving the reliability of synthetic estimates. Uncertainty is quantified through a parametric bootstrap method specifically tailored to the extended model. Under heterogeneous data-generating scenarios, the proposed method yields lower relative bias and relative root mean squared prediction error than existing approaches. The methodology is further illustrated using data from the 2002 Albania Living Standards Measurement Survey, combined with auxiliary information from the 2001 census, to estimate poverty indicators for 374 municipalities.

翻译：本研究扩展了高维参数嵌套误差回归模型（NERHDP），以应对小区域贫困估计中的挑战。我们提出了一个稳健且灵活的框架，用于推导小区域贫困指标的经验最优预测值（EBPs），同时适应不同区域间回归系数和抽样方差的异质性。为缓解现有算法的计算局限，本文引入了一种高效的估计程序，显著减少了计算时间，并增强了对大规模数据集的可扩展性。此外，我们还开发了一种针对样本外区域生成区域特异性贫困估计的新方法，从而提高了合成估计的可靠性。通过专门为扩展模型设计的参数自助法，对估计的不确定性进行了量化。在异质性数据生成情景下，与现有方法相比，所提方法具有更低的相对偏差和相对均方根预测误差。本文进一步以2002年阿尔巴尼亚生活水平测量调查数据为基础，结合2001年人口普查的辅助信息，对374个城市的贫困指标进行了估计，以演示该方法的应用。