A New Approach to Sampling from Finite Populations. II Distribution-Free Sufficiency
有限总体抽样的新方法（二）：分布无关充分性AI 解读 ↓
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有限总体抽样的新方法（二）：分布无关充分性
- 研究问题
- 当有限总体抽样中的先验知识可表示为一类先验分布时，如何将线性充分性扩展为适用于全部估计量的充分性？
- 方法与思路
- 作者取消原有充分性定义的线性限制，定义分布无关充分性，并研究总体总量估计量及两种充分性之间的关系。
- 材料陈述的贡献
- 摘要称前篇的某个线性总量估计量也满足扩展后的充分性准则；限制在线性估计量类内时，两种充分性一致。
- 阅读关注点
- 应核对先验分布类如何进入充分性定义、特定总量估计量的形式，以及线性与分布无关充分性等价的精确范围。
- 阅读边界
- 仅据所给 Crossref 摘要；前篇定义、估计量形式及先验分布类限制未提供，不能将结果理解为无条件充分性。
原文摘要
Summary The idea that in some situations the prior knowledge about the unknown parameters could be formulated as a class of prior distributions, which could be used, not necessarily through Bayes posterior probability, for subsequent inference, is already present in Godambe (1955). In the present paper, the concept of distribution-free linear sufficiency or in short linear sufficiency, originally due to Barnard (1963b) but redefined by the present author (Part I), is extended by defining distribution-free sufficiency, removing the restriction of linearity. This extension again is based on the assumption that in some situations prior knowledge could be formulated as a class of prior distributions. A certain linear estimator of the population total, which in Part I was shown to satisfy the redefined criteria of linear sufficiency uniquely in the class of all linear estimators, is now shown to satisfy this extended criteria of distribution-free sufficiency in the entire class of estimators. Further the general relationship between the linear sufficiency of Part I and the distribution-free sufficiency introduced here is investigated. Broadly the result is that, if we restrict to linear estimators only, distribution-free sufficiency is identical with linear sufficiency. Finally, some remarks are offered by way of comparison between the result obtained by the author previously (Godambe, 1955) and the result here, about the utilization of the prior information. The approach of this paper clearly implies a generalization of Fisherian sufficiency suitable for the situations when prior knowledge consists of a class of prior distributions. An alternative generalization when the prior knowledge consists of a group structure is due to Barnard (1963a).