A Likelihood Analysis of the Linear Calibration Problem

Abstract

In the linear calibration problem, when the regression variable y is related to the independent variable x by the equation

likelihood methods are used to make inferences about an unknown value of x given the corresponding observed values of y and previous observed pairs (y, x). Krutchkoff's suggestion of using an inverse estimator for the unknown r, in place of the classical maximum likelihood estimator is discussed from the point of view of the likelihood approach. From a likelihood point of view the question of which estimator is better turns out to be of little importance. It is also found that a good number of the cases considered by Krutchkoff give non-informative likelihood functions, but cases which the authors feel are more common in practice tend to give likelihood functions which are informative and approximately normal in shape.

KEY WORDS:

• Likelihood
• Marginal Likelihood
• Calibration
• Maximum Likelihood Estimate
• Inverse Estimate