商业调查中小领域的稳健估计
Robust estimation for small domains in business surveys
摘要：
小范围（或小领域）估计仍然很少用于商业统计，因为诸如营业额等变量的偏斜性和可变性带来了挑战。我们研究了一系列的小面积估计方法的基础上，估计在荷兰零售业的行业活动。我们使用税务登记数据和抽样程序，复制荷兰统计局的结构性商业调查的零售部门的抽样调查的基础上，小面积估计的属性。特别是，我们考虑使用的EBLUP下的随机效应模型和衍生的EBLUP的变化下（a）一个随机效应模型，包括一个复杂的规格的水平1方差和（b）一个随机效应模型，通过使用调查权重拟合。虽然在估计中考虑调查权重很重要，但在这种情况下，有影响力的数据点的影响仍然是主要挑战。本文进一步探讨了使用离群稳健估计在商业调查，特别是一个强大的版本的EBLUP，M-回归为基础的合成估计，和M分位数小区域估计。后者家庭的小面积估计包括强大的投影（没有和调查权重）和强大的预测版本。M分位数方法具有最低的经验均方误差，并大大优于直接估计，但在实践中如何选择调整常数的偏差调整是一个悬而未决的问题。本文通过探索一种双重稳健的方法，包括在小面积估计中使用调查权重与离群稳健方法，做出了进一步的贡献。
英文摘要：
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 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, though 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.
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