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
- 当样本辅助变量均值偏离已知总体均值时，如何在简单随机抽样框架内修正比率估计及其方差的条件偏差？
- 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分布，近似条件分布，构造偏差调整与条件方差公式。
- 材料陈述的贡献
- 摘要称，无须额外采用预测模型，也可在简单随机抽样假设下得到条件调整；两个总体的模拟用于展示改善并比较方法。
- 阅读关注点
- 应核对条件偏差的定义、联合正态近似所需条件、调整项的估计，以及辅助变量严重不平衡时近似是否仍可靠。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，不能推断刊本变化；条件调整是近似结果，其有限样本精度和适用范围未充分说明。
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.