Heteroscedastic controlled calibration model applied to analytical chemistry

TL;DR

This paper introduces a new heteroscedastic controlled calibration model for chemical analysis, accounting for measurement errors in the independent variable, and compares its performance with traditional models through simulations and real applications.

Contribution

It proposes a novel calibration model that considers errors in the controlled independent variable, improving accuracy in chemical concentration estimations.

Findings

The new model performs better than traditional calibration models in simulations.

Simulation results show improved estimator properties with the new model.

Applications demonstrate the model's effectiveness in real chemical analysis scenarios.

Abstract

In chemical analysis made by laboratories one has the problem of determining the concentration of a chemical element in a sample. In order to tackle this problem the guide EURACHEM/CITAC recommends the application of the linear calibration model, so implicitly assume that there is no measurement error in the independent variable $X$. In this work, it is proposed a new calibration model assuming that the independent variable is controlled. This assumption is appropriate in chemical analysis where the process tempting to attain the fixed known value $X$ generates an error and the resulting value is $x$, which is not an observable. However, observations on its surrogate $X$ are available. 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.