Heteroscedastic controlled calibration model applied to analytical chemistry

• Published in: Journal of chemometrics Vol. 24; no. 5; pp. 241 - 248
• Main Authors: Blas, Betsabé, Sandoval, Mônica C.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.05.2010; Wiley; Wiley Subscription Services, Inc
• Subjects: Analytical chemistry; Calibration; Chemical analysis; Chemical elements; Chemistry; Chemometrics; controlled variable; Error analysis; Errors; Estimators; Exact sciences and technology; General and physical chemistry; General. Nomenclature, chemical documentation, computer chemistry; Independent variables; Laboratories; linear calibration model; measurement error model; Simulation; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry; uncertainty; Analytical chemistry; Uncertainty; Chemical analysis; linear calibration model; Calibration; Laboratory; Chemical element; Simulation; Models; measurement error model; Chemometrics; Measurement error; controlled variable
• ISSN: 0886-9383; 1099-128X; 1099-128X
• DOI: 10.1002/cem.1275

In chemical analyses performed by laboratories, one faces the problem of determining the concentration of a chemical element in a sample. In practice, one deals with the problem using the so‐called linear calibration model, which considers that the errors associated with the independent variables are negligible compared with the former variable. In this work, a new linear calibration model is proposed assuming that the independent variables are subject to heteroscedastic measurement errors. A simulation study is carried out in order to verify some properties of the estimators derived for the new model and it is also considered the usual calibration model to compare it with the new approach. Three applications are considered to verify the performance of the new approach. Copyright © 2010 John Wiley & Sons, Ltd. In this paper the problem of determining the concentration of a chemical element in a sample is treated through a new linear calibration model assuming that the independent variables are subject to heteroscedastic measurement errors. A simulation study is carried out in order to verify some properties of the maximum likelihood estimators. Three applications are considered to verify the performance of the new approach.