Choice of Statistical Calibration Procedures When the Standard Measurement in Also Subject to Error

Abstract

This paper considers a statistical calibration problem in which the standard as well as the nonstandard measurement is subject to error. Since the classical approach cannot handle this situation properly, a functional relationship model with additional feature of prediction is proposed. For the analysis of the problem four different approaches-two estimation techniques (ordinary and grouping least squares) combined with two prediction methods (classical and inverse prediction)-are considered. By Monte Carlo simulation the performance of each approach is assessed in terms of the probability of concentration. The simulation results indicate that the ordinary least squares with inverse prediction is generally preferred in interpolation while the grouping least squares with classical prediction turns out to be better in extrapolation.