Combining Independent Studies in a Calibration Problem
研究了响应变量由k种不同方法或仪器测量时的校准问题，提出将经典估计量线性组合，证明当k≥2时组合估计量均值有限，k≥3时均方误差有限，并给出了渐近偏差和均方误差表达式及两种置信集。
Abstract The problem of calibration in which the response variable is measured by k different methods or using different instruments is considered. It is well known that the usual classical estimator for the unknown explanatory variable has infinite mean and mean squared error when k = 1. In this article a linear combination of the classical estimators is proposed. It is shown that the combined estimator has finite mean provided that k ≥ 2 and finite mean squared error provided that k ≥ 3. Expressions for asymptotic bias and mean squared error are given. Also, two confidence sets for the unknown exploratory variable are developed sufficient conditions under which they will be finite intervals are given. The results are illustrated by a practical example.