A Comparison of Classical and Inverse Estimators in the Calibration Problem

Abstract

Deciding between classical and inverse regression estimators in a calibration setting has been a dilemma for applied statisticians for over three decades. One proposed resolution of this dilemma compares estimators of a predicted-value of the regressor variable based on an observed value of the dependent variable through the Pitman closeness criterion. Least squares and inverse least squares techniques are compared via simulation due to the complexity of the distribution used in the calculation, which depends upon the product of a linear and a quadratic form. We show that the inverse least squares procedure provides an estimator which is Pitman-closer to the calibration point, x ₀, than the corresponding classical least squares approach when the calibration point is not too close to the sample average. We show the usefulness of this dominance in practical terms through an example, which involves leak detection in product transmission lines.

Keywords:

• Leak detection
• Pitman closeness
• Transmission lines

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62P30