Estimating the Size of a Subdomain: An Application in Auditing
提出一种替代比率估计量的方法，用于估计总体中子域的总规模，以审计中非免税销售交易额的估计为例，通过超总体模型推导出一族估计量，模拟实验表明最优估计量在多数情况下优于比率估计量。
This article suggests an alternative to the ratio estimator for estimating the total size of a subdomain of a population. The application that served as the genesis for this work is from auditing. The problem is to estimate the total of sales transactions that are not tax exempt from an audit sample of the population of nontaxed sales transactions. A superpopulation approach, which models the unit's probability of belonging to the subdomain as a function of its size, leads to a family of estimators. The simplest member of this famiiy is one in which that function is specified to be a constant. The optimal estimator for this model performs markedly better than the ratio estimator when the assumption is true and often performs better when it is not, though in that case it is biased. Stratification is shown to reduce this bias and at the same time make the ratio estimator more similar to the optimal estimator. A simulation experiment shows that the theoretical advantages hold in a real audit population.