Poverty mapping is used to facilitate efficient allocation of aid resources, with the objective of ending poverty, the first of the United Nations Sustainable Development Goals. Levels of poverty across small geographic domains within a country are estimated using a statistical model, and the resulting estimates displayed on a poverty map. Current methodology for small area estimation of poverty utilises various forms of regression modelling of household income or expenditure. Fitting sound models requires skill and time, especially where there are many candidate regressors and even more possible interactions. Tree‐based methods have the potential to screen more quickly for interactions and also to provide reliable small area estimates in their own right. A classification tree technique has been presented by Bilton et al. (Comput Stat Data Anal115: 53–66, 2017) for estimating poverty incidence, but although adjustments were made to incorporate complex survey designs and estimate mean square error, classification trees are unable to estimate the associated non‐categorical deprivation measures of poverty gap and poverty severity. The focus of this paper is regression trees, because they enable all three core poverty measures of incidence, gap and severity to be estimated. Using regression trees, two alternative methodologies, parametric and non‐parametric, are explored for producing household level predictions that are then amalgamated up to small‐area level. New methods are developed for mean square error estimation. The properties of the small area estimates based on these regression tree techniques are then evaluated and compared with linear mixed models both by simulation and by using real poverty data from Nepal.

中文翻译：

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贫困图的回归树

绘制贫困图用于促进有效分配援助资源，目的是消除贫困，这是联合国可持续发展目标的第一个目标。使用统计模型估算一个国家/地区中较小地理区域的贫困水平，并将所得的估计结果显示在贫困图中。当前的小面积贫困估计方法利用各种形式的家庭收入或支出回归模型。拟合声音模型需要技巧和时间，尤其是在存在许多候选回归因子和甚至更多可能交互作用的地方。基于树的方法有可能更快地进行交互筛选，并且可以自行提供可靠的小区域估计。Bilton等人提出了一种分类树技术。（计算统计资料肛门115：2017年，第53-66页）来估计贫困发生率，但是尽管进行了调整以纳入复杂的调查设计并估计均方误差，但是分类树无法估计相关的非分类剥夺措施中的贫困差距和贫困严重程度。本文的重点是回归树，因为回归树可以估计发病率，差距和严重性的所有三个核心贫困指标。使用回归树，探索了两种替代方法，参数化和非参数化，以产生家庭水平的预测，然后将其合并到小区域水平。开发了用于均方误差估计的新方法。