Mixing of direct, ratio, and product method estimators
Mixing of direct, ratio, and product method estimators
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混合直接法、比率法和乘积法估计器
DOI：
10.1111/j.1467-9574.1980.tb00703.x
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发表时间：
1980
期刊：
影响因子：
--
通讯作者：
J. Vos
中科院分区：
文献类型：
--
作者：
J. Vos
在 SrivenkataramanaTracy 的一篇论文中[4]，介绍了四种使用辅助变量估计总体总 Y 的方法，给定一个随机样本，无需从该总体中进行替换。这些方法“是围绕这样的想法建立的：估计总体总数本质上相当于估计非样本单位对应的总数，因为一旦抽取样本并对其进行测量，就知道与样本单位相对应的总数。”然而，在样本比例较小的情况下，非样本单位构成了总体的大部分，并且预计不会比传统估计量有很大的改进。因此，将这些方法与现有的估计器进行比较，结果发现它们是本文介绍的“混合估计器”的特例。后者的估计量可以渐近地等价于回归估计量，因此渐近优于所有其他估计量。对[4]中给出的仿真例子进行了精确的比较。本文中的陈述“在小样本情况下，建议的估计量优于回归估计量，其性能优越”显然具有误导性。最后与其他“混合型”估计器进行了比较，这在实践中非常有用。
In a paper by SrivenkataramanaTracy[4], four methods of estimating a population total Ywith the use of an auxiliary variable were introduced, given a random sample without replacement from that population. These methods were “built around the idea that estimating the population total is essentially equivalent to estimating the total corresponding to the non‐sample units, since that corresponding to the sample units is known once the sample is drawn and measurements are made on it.” However, in the case of small sampling fractions the nonsample units constitute most of the population and no great improvement over the traditional estimators is to be expected. Therefore the methods are compared with the existing estimators and it turns out that they are special cases of the “mixing estimators”, introduced in this paper. The latter estimators can be made asymptotically equivalent to the regression estimator and are therefore asymptotically superior to all other estimators. An exact comparison is carried out on the artificial example given in [4]. The statement in this paper that “the proposed estimators are to be preferred to the regression estimator for., superiority of performance in the case of small samples” is evidently misleading. Finally a comparison is made with other “mixing‐type” estimators, that can prove very useful in practice.