Several methods have been devised to mitigate the effects of outlier values on survey estimates. If outliers are a concern for estimation of population quantities, it is even more necessary to pay attention to them in a small area estimation (SAE) context, where sample size is usually very small and the estimation in often model based. In this paper we set two goals: The first is to review recent developments in outlier robust SAE. In particular, we focus on the use of partial bias corrections when outlier robust fitted values under a working model generate biased predictions from sample data containing representative outliers. Then we propose an outlier robust bootstrap MSE estimator for M-quantile based small area predictors which considers a bounded-block-bootstrap approach. We illustrate these methods through model based and design based simulations and in the context of a particular survey data set that has many of the outlier characteristics that are observed in business surveys.

已经设计了几种方法来减轻异常值对调查估计值的影响。如果离群值是估计种群数量的一个关注点，则在小面积估计（SAE）的情况下（在样本量通常很小且估计值通常基于模型的情况下），甚至更有必要注意这些异常值。在本文中，我们设定了两个目标：首先是回顾异常健壮的SAE的最新发展。特别是，当工作模型下的离群鲁棒拟合值从包含代表性离群点的样本数据生成偏向预测时，我们专注于部分偏向校正的使用。然后，我们针对基于M分位数的小区域预测器提出了一种异常鲁棒自举MSE估计器，该估计器考虑了有界块自举方法。