A Comparison of Classical and Inverse Estimators in the Calibration Problem

• Published in: Communications in statistics. Theory and methods Vol. 36; no. 1; pp. 83 - 95
• Main Authors: Kannan, Nandini, Keating, Jerome P., Mason, Robert L.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01-01-2007; Taylor & Francis
• Subjects: Exact sciences and technology; General topics; Leak detection; Linear inference, regression; Mathematical foundations; Mathematics; Nonparametric inference; Pitman closeness; Primary 62J05; Probability and statistics; Sciences and techniques of general use; Secondary 62P30; Statistics; Transmission lines; Linear form; Pitman closeness; Primary 62J05; Average; Dependent variable; Mean estimation; Leak detection; Inverse problem; Statistical method; Statistical regression; Transmission lines; Model matching; Least squares method; Distribution function; Secondary 62P30; Simulation model; Quadratic form
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920600966225

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.