Conditioning Ratio Estimates Under Simple Random Sampling
简单随机抽样下比率估计的条件化调整AI 解读 ↓
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简单随机抽样下比率估计的条件化调整
- 研究问题
- 简单随机抽样中，当样本在辅助变量上不平衡时，如何修正总体均值比率估计及其方差估计的条件偏差？
- 方法与思路
- 作者利用目标变量与辅助变量样本均值的渐近联合正态性，构造给定辅助变量均值的近似条件分布与偏差调整。
- 材料陈述的贡献
- 摘要称提出偏差调整估计和条件方差公式，并用两个总体的模拟说明改进及与基于预测模型的既有方法的比较。
- 阅读关注点
- 应核对条件化对象、总体辅助均值的可用性、联合正态近似条件，以及模型成立与不成立时的模拟设计和偏差表现。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；近似有效范围和模拟数值未给出，不能认定调整普遍有效或推断刊本变化。
原文摘要
The usual ratio estimates for a population mean use information on an auxiliary variable to improve the estimation. The standard randomization analysis, however, does not take enough account of the observations on the auxiliary variable, so estimates and estimated variates can be conditionally biased unless the sample is balanced with respect to the auxiliary variable. I propose a method of adjustment for the bias of the estimate and its variance based only on the assumption of simple random sampling, which uses an approximate conditional distribution of the estimate given the mean of the auxiliary variable. Roy all and Cumberland (1981) illustrated empirically that the usual random sampling estimates and estimated variances could be badly conditionally biased when samples were obtained that were unbalanced in the auxiliary variate. So if the sample mean and population mean, both of which are known at the time of analysis, are not close, it is known that the results are biased, but the usual random sampling formulas, which are purely unconditional, do not take account of this. They suggested that prediction models were necessary to adjust these. If the joint distribution of the sample means of the variate and covariate are considered together, then using the fact that these are asymptotically bivariate normal, it is possible to adjust approximately for the linear regression of the variate mean on the mean of the auxiliary variate. In this way a bias-adjusted estimate is suggested and formulas for the conditional variances of the estimates are obtained. A simulation study of two populations, one where the model on which the ratio estimate is based holds and one where it does not, is carried out to illustrate the improvements given by the results and to compare them with results based on the formulas obtained by Royall and Cumberland (1981) by using prediction models, showing that results based on the assumption of simple random sampling can provide adequate theoretical results.