How Nearly Can Model-Based Prediction and Design-Based Estimation Be Reconciled?
模型预测与设计估计能够协调到何种程度？AI 解读 ↓
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模型预测与设计估计能够协调到何种程度？
- 研究问题
- 有限总体总量及其期望的模型预测，如何与设计型广义回归估计协调，回归参数估计和入样概率哪个更关键？
- 方法与思路
- 作者分别修改回归参数估计或入样概率，使两种模型预测与广义回归估计相协调，并用适当工具变量构造一般情形估计。
- 材料陈述的贡献
- 摘要称入样概率选择在渐近上更重要，保留最优入样概率的协调方式通常具有更小的渐近期望方差，并联系若干熟悉估计量。
- 阅读关注点
- 应核对两个预测目标的差别、最优入样概率的定义、方差比较条件，以及工具变量构造与特殊情形等价关系。
- 阅读边界
- 所给索引摘要未标稿件版本。摘要未列完整模型与渐近条件；工具变量在此服务于调查估计，不能据此推断因果识别结论。
原文摘要
Two general linear model-based predictors, one of the expectation of a finite population total and one of that total itself, are compared with the design-based generalized regression estimator (GRE). First, the predictors are made to conform to the GRE by modifying the regression parameter estimators but retaining the same (optimal) inclusion probabilities. Second, the GRE is made to conform with each of the predictors in turn by modifying the inclusion probabilities but retaining the generalized least squares (GLS) or best linear unbiased form for the estimators of the regression parameters. It is shown that the choice of inclusion probabilities is more important asymptotically than the choice of estimator for the regression parameters and hence that predictors obtained by the first method generally have smaller asymptotic expected variances than those obtained by the second method. Using the first method, certain special cases are shown to correspond to familiar estimators. If there is only one explanatory variable and no constant term in the model, the predictor of the expectation of the finite population total obtained by the first procedure is identical to the Horvitz-Thompson ratio estimator. If the finite population total itself is to be predicted, the estimator is that suggested by Brewer (1979). If there is a constant term in the model, the GLS predictor can be conformed to the GRE by replacing the inverse-variance weights used to estimate the regression coefficients by functions of the (optimal) inclusion probabilities. It is shown further that appropriate estimators can be constructed in the general case by the use of an appropriate instrumental variable. Under fairly weak conditions this variable can be constructed by deleting a column from a matrix used in the calculation of the GLS estimator and replacing it by a column of weights that are simple functions of the inclusion probabilities. Illustrative examples are given.