Calibration With Randomly Changing Standard Curves

Abstract

Changes in calibration curves from one time to the next, caused by drift, often require measuring devices to be recalibrated at frequent intervals. In such situations the usual practice is to estimate the unknown values of test samples using only data from the corresponding calibration period. Under a random coefficient regression model for the different calibration curves, however, it can be shown that it is more efficient to combine the data from all calibration periods to estimate the unknowns. We consider a particular class of point estimators obtained by inverting suitable prediction functions and show that the estimator obtained from a best prediction function is optimal in a sense defined by Godambe (1960) and Durbin (1960) in the context of unbiased estimating equations. We also compare the smallsample performance of this estimator with the usual estimator using the Pitman closeness criterion.

KEY WORDS:

• Pitman closeness
• Random coefficient models
• Unbiased estimating equations