Double Sampling for Exact Values in Some Multivariate Measurement Error Problems
本文在多元正态框架下，允许变量子集存在测量误差，通过双重抽样获取部分真实值，提出极大似然估计方法，并给出简单线性回归中的最优抽样率。
Abstract 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.