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Survey sampling and small-area estimation
Mathematical Population Studies ( IF 1.4 ) Pub Date : 2018-10-02 , DOI: 10.1080/08898480.2018.1507580
Enrico Fabrizi 1, 2 , Tomasz Ża̧dło 1, 2
Affiliation  

This issue is devoted to survey sampling methods. It carries on a tradition of Mathematical Population Studies, after the issues guest-edited by Malay Ghosh and Tomasz Ża̧dło (2014) and Vera Toepoel and Schonlau (2017). Wright (2001) presented some major moments of the history of survey sampling. He acknowledged the pioneering work of Pierre Simon de Laplace (1878-1912; Gillispie, 1997), who estimated the population size of France in 1802 based on a sample of communes, which were administrative districts. He multiplied the population size of the sampled communes by the ratio of the recorded total number of births for the whole country to the one recorded in the sample. He used the same method to estimate the population size of France for 1782. John Graunt (1665) had also used a similar calculus to estimate the population size of England in 1662. In design-based inference, introduced by Neyman (1934), the values taken by the variable of interest are considered as fixed and the sampling design is the only source of randomness affecting the estimates. In modelbased inference, the values taken by the variable of interest are considered as the realizations of random variables. The set of conditions defining the class of this distribution is called “super-population” model (Cassel et al., 1976: 80) and inference is made conditionally on the sample, which is either drawn at random or chosen purposively from the population. Accuracy is measured only over possible realizations of the variables. In model-assisted inference, the model is used to increase accuracy, but good design-based properties, such as design consistency, are of primary interest. Various methods include calibration estimators and pseudo-empirical best linear unbiased predictors. The accuracy of the former is evaluated through randomization techniques; the accuracy of the latter through a model. In the Bayesian framework, the estimator is a conditional expectation in the posterior distribution of the population or subpopulation parameters and the posterior variance is used as a measure of the variability of the Bayesian estimator. This Bayesian technique applies to continuous, binary, and count data.

中文翻译:

调查抽样和小区域估算

本期专门讨论调查抽样方法。在由Malay Ghosh 和Tomasz Ża̧dło (2014) 以及Vera Toepoel 和Schonlau (2017) 客座编辑的问题之后,它继承了数学人口研究的传统。Wright (2001) 展示了调查抽样历史的一些重要时刻。他承认皮埃尔·西蒙·德·拉普拉斯(Pierre Simon de Laplace,1878-1912 年;吉利斯皮,1997 年)的开创性工作,他根据作为行政区的公社样本估计了 1802 年法国的人口规模。他将抽样公社的人口规模乘以全国记录的出生总人数与样本中记录的出生人数之比。他用同样的方法估算了 1782 年法国的人口规模。约翰·格劳特 (John Graunt)(1665 年)也用类似的演算估算了 1662 年英国的人口规模。在 Neyman (1934) 引入的基于设计的推理中,感兴趣的变量所取的值被认为是固定的,抽样设计是影响估计的唯一随机性来源。在基于模型的推理中,感兴趣的变量所取的值被视为随机变量的实现。定义该分布类别的一组条件称为“超级人口”模型(Cassel 等人,1976:80),并且有条件地对样本进行推断,该样本要么随机抽取,要么有目的地从总体中选择。准确度仅在变量的可能实现上进行测量。在模型辅助推理中,模型用于提高准确性,但主要关注良好的基于​​设计的属性,例如设计一致性。各种方法包括校准估计器和伪经验最佳线性无偏预测器。前者的准确性通过随机化技术进行评估;后者通过模型的准确性。在贝叶斯框架中,估计量是种群或子种群参数的后验分布中的条件期望,后验方差被用作贝叶斯估计量可变性的度量。这种贝叶斯技术适用于连续、二进制和计数数据。估计量是总体或子种群参数的后验分布的条件期望,后验方差用作贝叶斯估计量可变性的度量。这种贝叶斯技术适用于连续、二进制和计数数据。估计量是总体或子种群参数的后验分布的条件期望,后验方差用作贝叶斯估计量可变性的度量。这种贝叶斯技术适用于连续、二进制和计数数据。
更新日期:2018-10-02
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