An Analysis of the Linear-Calibration Controversy From the Perspective of Compound Estimation

Abstract

The competing classical and inverse point estimators in statistical calibration can be obtained by direct or inverse regression and are to some extent supported by the maximum likelihood and Bayesian approaches, respectively. Both of these approaches depend on specific distributional assumptions, but these assumptions confuse the main issue because both estimators can be justified without reference to them. By using a compound estimation approach, it is shown that the classical estimator can be derived as a linear compound estimator satisfying the criterion of asymptotic unbiasedness, while the inverse estimator is a linear compound estimator without the unbiasedness constraint. This formulation requires neither specific distributional assumptions nor reference to direct or inverse regression. Assessments of the two estimators are made in terms of their performance in estimating the current x value. It is shown that superiority of the inverse estimator can only be guaranteed if the current x value is samp...