Combining Independent Information in a Multivariate Calibration Problem

The problem of combining independent information from different sources in a multivariate calibration setup is considered. The dimensions of the response vectors from various sources may be unequal. A linear combination of the classical estimators based on the individual sources is proposed as an estimator for the unknown explanatory variable. It is shown that the combined estimator has finite mean provided the sum of the dimensions of the response vectors exceeds one and has finite mean squared error if it exceeds two. Expressions for asymptotic bias and mean squared error are given.