We consider random forests and LASSO methods for model-based small area estimation when the number of areas with sampled data is a small fraction of the total areas for which estimates are required. Abundant auxiliary information is available for the sampled areas, from the survey, and for all areas, from an exterior source, and the goal is to use auxiliary variables to predict the outcome of interest. We compare areal-level random forests and LASSO approaches to a frequentist forward variable selection approach and a Bayesian shrinkage method. Further, to measure the uncertainty of estimates obtained from random forests and the LASSO, we propose a modification of the split conformal procedure that relaxes the assumption of identically distributed data. This work is motivated by Ghanaian data available from the sixth Living Standard Survey (GLSS) and the 2010 Population and Housing Census. We estimate the areal mean household log consumption using both datasets. The outcome variable is measured only in the GLSS for 3\% of all the areas (136 out of 5019) and more than 170 potential covariates are available from both datasets. Among the four modelling methods considered, the Bayesian shrinkage performed the best in terms of bias, MSE and prediction interval coverages and scores, as assessed through a cross-validation study. We find substantial between-area variation, the log consumption areal point estimates showing a 1.3-fold variation across the GAMA region. The western areas are the poorest while the Accra Metropolitan Area district gathers the richest areas.

翻译：本文考虑在抽样数据覆盖区域仅占需估计总区域一小部分的情况下，采用随机森林和LASSO方法进行基于模型的小区域估计。从调查中可获得抽样区域的丰富辅助信息，而外部数据源则提供所有区域的辅助变量，研究目标在于利用辅助变量预测目标结果变量。我们将区域层面的随机森林和LASSO方法与频率学派向前变量选择方法及贝叶斯收缩方法进行比较。为衡量随机森林和LASSO估计的不确定性，我们提出了一种改进的分裂保形程序，该程序放宽了数据同分布的假设。本研究基于加纳第六次生活标准调查（GLSS）和2010年人口与住房普查数据展开，利用两组数据集估计区域平均家庭对数消费。结果变量仅在GLSS中测量，覆盖全部区域中的3%（5019个区域中的136个），两组数据集共提供170余个潜在协变量。在四种建模方法中，交叉验证评估显示贝叶斯收缩方法在偏差、均方误差、预测区间覆盖率和得分方面表现最优。我们发现区域间存在显著差异，大阿克拉大都市区（GAMA）各区域的对数消费点估计值呈现1.3倍的变化幅度：西部地区最为贫困，而阿克拉都市区则聚集了最富裕区域。