The Errors of Lattice Sampling
格子抽样的误差AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要讨论一般调查抽样设计与抽样方差，未明确涉及所列经济计量细分领域。
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格子抽样的误差
- 研究问题
- 在多重分类中保持各主要类别或类别组合样本数平衡的格子抽样，如何计算和估计其抽样误差？
- 方法与思路
- 作者讨论利用完整总体数据计算抽样方差，以及利用特殊样本模式或多个互斥格子样本估计方差的方法。
- 材料陈述的贡献
- 摘要称，文章给出方形格子的严格公式证明，并将方差分量方法扩展至立方及一般格子，也讨论多阶段抽样。
- 阅读关注点
- 应核对不同选择方法中的随机化设计、样本方差估计的有效条件，以及格子维度和样本规模公式的原始排版。
- 阅读边界
- Crossref 摘要中的幂次排版不清，需查阅原 PDF，不能重构规模公式；摘要也指出部分设计的均值和误差估计可能不准确。
原文摘要
Summary Lattice samples are samples selected from a multiple classification of units with one unit in each subclass in such a way that they include equal numbers of units from each main class or from each combination of two, three or more main classes in different classifications. The present paper provides a discussion of the errors of such samples. Methods for determining the sampling variances from the complete data, when these are available, for purposes such as a comparison of different sampling methods, are described for several methods of selection. The estimation of the sampling variances from the sample data is also considered. In general estimates of error can be obtained (a) from samples consisting of special patterns of units or (b) from random samples of several mutually exclusive sets each of which itself constitutes a lattice sample. If suitable elements of randomization are introduced method (a) is satisfactory for selecting samples of 2p units from a p × p lattice, samples of 2p2 units from a p × p × p lattice and, in general, 2pn–1 units from a pn lattice. In other cases, however, the estimated means and errors may be inaccurate. Method (b) is most useful when several lattices have to be sampled. The case of the square lattice is considered in detail and rigorous proofs of the various formulae are given. In the section on cubic lattices a method is given whereby the required expressions can be written down immediately in terms of components of variance. This method is extended to the general case of sampling a pn lattice. Examples of rectangular lattices and multistage sampling are also briefly considered.