Comparison of the inverse and classical estimators in multi-univariate linear calibration

Abstract

The problem of estimation in the controlled linear calibration with a multivariate response and univariate explanatory variable is considered when the covariance matrix is unknown. It is shown that the classical estimator is inadmissible whereas the inverse estimator is admissible. Both estimators have been shown to be biased (underestimating).

Keywords:

• Admissibility
• Bayes risk
• biased estimators
• inverse regression
• multivariate normal
• shrinkage estimator