This paper introduces Mixed Effect Gradient Boosting (MEGB), which combines the strengths of Gradient Boosting with Mixed Effects models to address complex, hierarchical data structures often encountered in statistical analysis. The methodological foundations, including a review of the Mixed Effects model and the Extreme Gradient Boosting method, leading to the introduction of MEGB are shown in detail. It highlights how MEGB can derive area-level mean estimations from unit-level data and calculate Mean Squared Error (MSE) estimates using a nonparametric bootstrap approach. The paper evaluates MEGB's performance through model-based and design-based simulation studies, comparing it against established estimators. The findings indicate that MEGB provides promising area mean estimations and may outperform existing small area estimators in various scenarios. The paper concludes with a discussion on future research directions, highlighting the possibility of extending MEGB's framework to accommodate different types of outcome variables or non-linear area level indicators.

翻译：本文提出了混合效应梯度提升（MEGB），该方法将梯度提升与混合效应模型的优势相结合，以处理统计分析中常见的复杂层次化数据结构。本文详细阐述了方法论基础，包括对混合效应模型和极限梯度提升方法的回顾，进而引出MEGB的引入。重点展示了MEGB如何从单元级数据推导出区域级均值估计，并利用非参数自助法计算均方误差（MSE）估计。通过基于模型和基于设计的模拟研究，本文评估了MEGB的性能，并将其与已有的估计方法进行了比较。研究结果表明，MEGB能提供有前景的区域均值估计，并在多种场景下可能优于现有小区域估计方法。本文最后讨论了未来研究方向，强调了将MEGB框架扩展以适配不同类型的结果变量或非线性区域级指标的可能性。