The paper delineates a proper statistical setting for defining the sampling design for a small area estimation problem. This problem is often treated only via indirect estimation using the values of the variable of interest also from different areas or different times, thus increasing the sample size. However, let us suppose the domain indicator variables are available for each unit in the population. In that case, we can define a sampling design that fixes the small-area samples sizes, thereby significantly increasing the accuracy of the small area estimates. We can apply this sampling strategy to business surveys, where the domain indicator variables are available in the business register and even household surveys, where we can have the domain indicator variables for the geographical domains.

翻译：本文阐明了为小区域估计问题定义抽样设计的适当统计框架。该问题通常仅通过利用感兴趣变量在不同区域或不同时间的取值进行间接估计来处理，从而增加样本量。然而，假设总体中每个单元都有域指示变量可用。在这种情况下，我们可以定义一个抽样设计，固定小区域的样本量，从而显著提高小区域估计的精度。这种抽样策略可应用于商业调查（其中商业登记册中提供了域指示变量），甚至家庭调查（其中我们可以获得地理域的域指示变量）。