Technometrics, Vol. 20 No.2 pp. 201-205

Elimination of the Bias in the Course of Calibration

Published by the American Society for Quality Control and the American Statistical Association

Laszlo J. Naszodi

Institute of Isotopes of the Hungarian Academy of Sciences

Abstract: Attention is drawn to a bias occuring in the course of calibration. Since the usual assumption of normality leads to an estimate without expected value, here a class of distribution is introduced which does not cause such a deficiency. Even in this class, the correction of the regression line defined with the help of standards might be necessary before estimating the abscissa value belonging to an unknown object. The estimate introduced is compared to the classical and inverse estimates. A mode of eliminating the error by experimental design is also discussed. The calibration process was simulated by computer.

This is my most cited publication. For example, in Journal of Quality Technology Volume 34 · Issue 1 · January 2002 (http://www.asq.org/pub/jqt/past/vol34_issue1/qtec-71.html) Edna Schechtman, Beer Sheva, and Cliff Spiegelman wrote:

“Naszodi (1978) derived a new estimator which is approximately (asymptotically) unbiased, more efficient than the classical estimator, and consistent.”

Another citation by James J. McKeon and Raj S. Chhikara, in LINEAR REGRESSION ESTIMATORS IN SAMPLE SURVEYS UNDER CALIBRATION p. 286:

“… the classical estimator has infinite variance. This serious defect can be removed by using a modified classical estimator proposed by Naszodi (1978).
… a modified estimator of X is obtained by X = x – (Y – y)/b(1 + q). This estimator has finite variance and is unbiased to 0(1/n).”

More citation by Christine Osborne, in Statistical Calibration: A Review International Statistical Review Vol. 59, No 3. (December 1991) pp. 309-336