Double Sampling for Exact Values in Some Multivariate Measurement Error Problems
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多元测量误差问题中获取真值的二阶段抽样
- 研究问题
- 当代理变量与真值维度不同、误差关系也不满足经典加性形式时，如何借助部分样本真值校正回归估计？
- 方法与思路
- 作者在多元正态框架下建立真值与代理值的回归关系，对随机抽取的子样本获取真值，并开展受限与非受限极大似然估计。
- 材料陈述的贡献
- 摘要称推导了估计量及其渐近性质，并在简单线性回归中确定成本约束下使斜率估计方差最小的二阶段抽样比例。
- 阅读关注点
- 应核对校准关系的识别条件、验证子样本的随机抽取要求，以及最优抽样比例依赖的成本结构和未知参数。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；结果置于多元正态框架，摘要未说明偏离该框架或非随机验证样本时的性质。
原文摘要
Increasing attention is being given to measurement error models in which the dimension of the proxy or surrogate values is different from that of the missing true values. Even if they are of the same dimension, the error model may not be the simple additive one of observed = true + error, where the error has mean 0. The use of broader models relating true and observed values requires the use of external or internal data containing some true values to calibrate/validate the measurement error model. This article considers a multivariate normal framework in which measurement error is allowed in any subset of the variables with a broad class of multivariate regression models relating true and observed values. The classical additive model is a special case. Multiple regression with random regressors (the structural case) is treated within this framework. Correcting for measurement error is made possible through double sampling in which true values are obtained for a randomly chosen subset of the main study units. Maximum likelihood estimators and their asymptotic properties are developed for both unrestricted and restricted models, where the latter arise through specific assumptions about the nature of the measurement error. Detailed results are given for simple linear regression in which case optimal double sampling rates are determined for estimating the slope with minimum variance subject to cost considerations. An example is presented based on the use of infrared measurements as surrogates for characteristics of wheat.