Small area (or small domain) estimation is still rarely applied in business statistics, because of challenges arising from the skewness and variability of variables such as turnover. We examine a range of small area estimation methods as the basis for estimating the activity of industries within the retail sector in the Netherlands. We use tax register data and a sampling procedure which replicates the sampling for the retail sector of Statistics Netherlands’ Structural Business Survey as a basis for investigating the properties of small area estimators. In particular, we consider the use of the empirical best linear unbiased predictor (EBLUP) under a random effects model and variations of the EBLUP derived under (a) a random effects model that includes a complex specification for the level 1 variance and (b) a random effects model that is fitted by using the survey weights. Although accounting for the survey weights in estimation is important, the impact of influential data points remains the main challenge in this case. The paper further explores the use of outlier robust estimators in business surveys, in particular a robust version of the EBLUP, M‐regression‐based synthetic estimators and M‐quantile small area estimators. The latter family of small area estimators includes robust projective (without and with survey weights) and robust predictive versions. M‐quantile methods have the lowest empirical mean squared error and are substantially better than direct estimators, although there is an open question about how to choose the tuning constant for bias adjustment in practice. The paper makes a further contribution by exploring a doubly robust approach comprising the use of survey weights in conjunction with outlier robust methods in small area estimation.

中文翻译：

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在业务调查中对小域进行可靠的估计

由于诸如营业额等变量的偏度和可变性带来的挑战，小面积（或小领域）估计仍然很少应用于商业统计中。我们研究了一系列小面积估算方法，作为估算荷兰零售业中各行业活动的基础。我们使用税务登记数据和抽样程序来复制荷兰统计局的结构性业务调查的零售部门的抽样，作为调查小面积估算器属性的基础。特别是，我们考虑在随机效应模型下使用经验最佳线性无偏预测因子（EBLUP），并根据（a）随机效应模型得出的EBLUP变异进行分析，该模型包括针对1级方差的复杂规范，以及（b）随机效应使用调查权重拟合的模型。尽管在估算中考虑调查权重很重要，但是在这种情况下，有影响力的数据点的影响仍然是主要挑战。本文进一步探讨了在商业调查中使用异常鲁棒估计量，特别是EBLUP的鲁棒版本，基于M回归的综合估计量和M分位数小面积估计量。后者的小面积估算器系列包括稳健的投影（不包括调查权重）和稳健的预测版本。M分位数方法的经验均方误差最低，并且比直接估计器要好得多，尽管在实践中如何选择调整常数来进行偏差调整还有一个悬而未决的问题。本文通过探索双重鲁棒性方法做出了进一步的贡献，该方法包括在小面积估计中结合使用调查权重和离群鲁棒性方法。