Method comparison on estimation for an unknown specimen in a heteroscedastic controlled calibration model
In analytical chemistry applications, statistical calibration models are commonly used to estimate the true value of an unknown specimen. In this article, we consider a heteroscedastic controlled calibration model in which both dependent and independent variables are subject to heteroscedastic measurement errors. The main task of using this model is to estimate the true value of an unknown regressor (independent variable) under the condition that a set of observations on its corresponding response (dependent variable) is available. We introduce four estimation methods to the problem of interest, including generalized least squares (GLS), modified least squares, corrected score, and expectation maximization-based (EM-based) methods. Furthermore, an interval estimation based on an asymptotic method is also derived. We compare their performance through detailed simulation studies. In consequence, GLS and EM-based methods are recommended in practical use. A real data example is given to illustrate the application of the calibration model. Copyright (c) 2013 John Wiley & Sons, Ltd.
calibration experiment least squares estimation likelihood function measurement error model unbiased estimating equation