The main object of this paper is to consider maximum likelihood estimators for models used in detection of analytical bias. We consider the regression model proposed in Ripley and Thompson (Analyst, 112, 1987, p. 377) with an EM-type algorithm for computing maximum likelihood estimators and obtain consistent estimators for the asymptotic variance of the maximum likelihood estimators, which seems not to be available in the literature. Wald type statistics are proposed for testing hypothesis related to the bias of the analytical methods with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. The main conclusion is that proposed approaches in the literature underestimate the covariance matrix of the maximum likelihood estimators. Results of simulation studies and applications to real data sets are reported to illustrate comparisons with other approaches.
SUMMARYRegression techniques are commonly applied to compare two or more analytical methods at several concentration levels. The paper considers consistent estimation in measurement error models with known different variances typically used in such situations. The approach is based on the corrected score methodology, which allows the derivation of consistent estimators for the model parameters and also for the asymptotic covariance matrix of the parameter estimators. Thus, Wald type statistics are proposed for testing hypothesis related to the bias of the analytical methods with the asymptotic chi-square distribution, which guarantees correct asymptotic significance levels. Results of small-scale simulation studies are reported to illustrate comparisons with other approaches. Applications to real data sets are also considered.
Detecting analytical bias is a valuable step during method validation and, in the case of the mining industry, fundamental when one validates the geological databases used for resource estimation. This will generally affect the costs of future investments in new or expanding projects. This paper details frequently used techniques for doing this, with their theoretical background, advantages and shortcomings, providing a deeper insight in how to choose a method for special applications. This is done by means of a review of the specialised literature, and by showing practical applications. The latter is done by choosing some of the most commonly used methods, comparing them using Monte Carlo simulations and testing in some real applications (analytical methods used in Brazilian prospects for copper, gold and iron). Consequently, laboratory specialists will have a better understanding of statistical tools for this purpose, being able to provide their customers with a very consistent assurance of chemical analytical results. It is shown that some commonly used statistical methods for this type of comparison are not applicable, and in some cases, one must resort to more complicated models. These are, however, easily implemented computationally, and the mathematical details are shown.
The main goal of this paper is to consider maximum likelihood inference for models used in the detection of analytical bias in the comparison of two or more methods of measurement. We embrace a functional errors-in-variables regression model with an EM-type algorithm for computing maximum likelihood estimates and to obtain consistent estimators for the asymptotic variance of the maximum likelihood estimators, which seems not to be found in the literature. Wald-type statistics are proposed for testing hypotheses related to the bias of the analytical methods with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. Some approaches specific for the two-methods comparison problem are not directly extendable to this more general situation. Results of simulation studies and an application to a real data set are also reported.
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