发表机构
Institut Teknologi Sepuluh Nopember（十November理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将多元自适应回归样条（MARS）整合进小域估计（SAE）框架，提出MARS-SAE模型，以处理非线性贫困数据，相比Fay-Herriot模型具有更高的效率和更低的误差，并保持可解释性。
AI 中文摘要
小域估计（SAE）建模通常用于解决调查样本有限区域中估计值不可靠的问题。然而，标准SAE模型（Fay-Herriot）只能适应线性模式，而在包括贫困在内的实际案例中，许多模式是非线性的。本研究提出在SAE框架内整合一种监督学习模型——多元自适应回归样条（MARS），即MARS-SAE，以应对直接估计不可靠的挑战，特别是在非线性情况下。超参数调优结果产生了最佳模型，其超参数组合如下：最大基函数（Max BF）=10，最大交互（MI）=2，最小观测数（MO）=1，惩罚项=3，广义交叉验证（GCV）=6.128。MARS-SAE表现出非常强的性能；实证上，该模型在降低估计误差方面更为高效，因为其相对效率（RE）高于SAE Fay-Herriot模型，并且在降低相对标准误差（RSE）方面也优于比较模型，同时其相对均方根误差（RRMSE）低于SAE Fay-Herriot模型（13.64%对13.75%）。MARS-SAE已被证明能够很好地捕捉非线性模式，同时保持可解释性，使其成为现象预测和诊断分析的有效工具。因此，鉴于爪哇岛是印度尼西亚（东盟地区最大的经济体）的战略区域，这项研究可以为该地区及东南亚的读者提供重要参考。
英文摘要
Small area estimation (SAE) modeling is often used to address the unreliability of estimates in areas with limited survey samples. However, standard SAE models (Fay-Herriot) can only accommodate linear patterns, whereas in real cases, including poverty, many patterns are nonlinear. This study proposes the implementation of a supervised learning model, multivariate adaptive regression splines (MARS), integrated within the SAE framework (MARS-SAE) to address the challenge of unreliable direct estimation, particularly in nonlinear cases. The hyperparameter tuning results yielded the best model with the following hyperparameter combinations: maximum basis function (Max BF) = 10, maximum interaction (MI) = 2, minimum observation (MO) = 1, penalty = 3, with general cross validation (GCV) = 6.128. MARS-SAE demonstrated very strong performance; empirically, the model proved more efficient at reducing estimation error due to its higher relative efficiency (RE) compared to the SAE Fay-Herriot model, as well as better reduction of relative standard error (RSE) than the comparison model, and it yielded a lower relative root mean squared error (RRMSE) compared to the SAE Fay-Herriot model (13.64% vs. 13.75%). MARS-SAE has been proven to capture nonlinear patterns very well while still maintaining interpretability, making it an effective tool for the predictive and diagnostic analyses of phenomena. Thus, this research can serve as an important reference for readers regionally and in Southeast Asia, given that Java Island is a strategic region for Indonesia, the largest economic power in the ASEAN region.
Comments20 pages, 3 figures
