Selectivity and error estimates in multivariate calibration: application to sequential ICP-OES

Bauer, Gottfried; Wegscheider, Wolfhard; Ortner, Hugo M.

doi:10.1016/0584-8547(91)80113-h

Cited by 32 publications

(16 citation statements)

References 32 publications

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“…In other words, the full S must be available. Successful application has been reported for the calibration of atomic spectra, e.g., obtained by inductively coupled plasma-optical emission spectrometry (ICP-OES) [27][28][29].…”

Section: Classical Vs Inverse Modelmentioning

confidence: 99%

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Olivieri

Faber²,

Ferré

et al. 2006

Pure and Applied Chemistry

322

166

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This paper gives an introduction to multivariate calibration from a chemometrics perspective and reviews the various proposals to generalize the well-established univariate methodology to the multivariate domain. Univariate calibration leads to relatively simple models with a sound statistical underpinning. The associated uncertainty estimation and figures of merit are thoroughly covered in several official documents. However, univariate model predictions for unknown samples are only reliable if the signal is sufficiently selective for the analyte of interest. By contrast, multivariate calibration methods may produce valid predictions also from highly unselective data. A case in point is quantification from near-infrared (NIR) spectra. With the ever-increasing sophistication of analytical instruments inevitably comes a suite of multivariate calibration methods, each with its own underlying assumptions and statistical properties. As a result, uncertainty estimation and figures of merit for multivariate calibration methods has become a subject of active research, especially in the field of chemometrics.

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Section: Classical Vs Inverse Modelmentioning

confidence: 99%

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Olivieri

Faber²,

Ferré

et al. 2006

Pure and Applied Chemistry

322

166

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“…with Gaussian distribution) and therefore the constant probability lines are circles and the radius (R) of these circles (which is here the standard deviation of the noise, often denoted by σ ε ) is independent from the sample composition and thus also from the actual absorbance values. (Note, however, that this assumption is not naturally valid for all analytical measurements [15,19].Definition of multichannel selectivity becomes, however, somewhat more complicated in other cases, and is not considered here for simplicity. )…”

Section: Error Inflationmentioning

confidence: 99%

“…In contrast to this, nearly all papers on multivariate selectivity [e.g., [13][14][15][16]) refer to equation systems which can be solved (have a unique solution) for the analyte concentration. This means also that they consider only one version of the classical method (ordinary least squares) where all bias is completely compensated.…”

Section: Bias and Selectivitymentioning

confidence: 99%

“…A IUPAC technical report [13], published twenty years later, in 2006, asserted that this selectivity criterion (which is essentially identical (see [13][14][15]) to that of Bergmann et al [8]), is the most suitable among those published. Very recently a review by Olivieri [16] confirms that this is still the prime selectivity measure in multivariate analysis.…”

Section: Multichannel Selectivity Concept Based On the Net Analyte Simentioning

confidence: 99%

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Comparison of the single channel and multichannel (multivariate) concepts of selectivity in analytical chemistry

Dorkó

Verbić

Horvai

2015

Talanta

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Cite this article as: Zsanett Dorkó, Tatjana Verbić and George Horvai, Comparison of the single channel and multichannel(multivariate) concepts of selectivity in analytical chemistry, Talanta, http://dx.doi.org/10.1016/j.talanta. 2015.02.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. www.elsevier.com This accepted author manuscript is copyrighted and published by Elsevier. AbstractDifferent measures of selectivity are in use for single channel and multichannel linear analytical measurements, respectively. It is important to understand that these two measures express related but still distinctly different features of the respective measurements. These relationships are clarified by introducing new arguments. The most widely used selectivity measure of multichannel linear methods (which is based on the net analyte signal, NAS, concept) expresses the sensitivity to random errors of a determination where all bias from interferents is computationally eliminated using pure component spectra. The conventional selectivity measure of single channel linear measurements, on the other hand, helps to estimate the bias caused by an interferent in a biased measurement. In single channel methods expert knowledge about the samples is used to limit the possible range of interferent concentrations. The same kind of expert knowledge allows improved (lower mean squared error, MSE) analyte determinations also in "classical" multichannel measurements if those are intractable due to perfect collinearity or to high noise inflation. To achieve this goal bias variance tradeoff is employed, hence there remains some bias in the results and therefore the concept of single channel selectivity can be extended in a natural way to multichannel measurements. This extended definition and the resulting selectivity measure can also be applied to the so-called inverse multivariate methods like partial least squares regression (PLSR), principal component regression (PCR) and ridge regression (RR).

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“…-A complete error model for (locally) linear systems is outlined that was recently introduced [7]. be different for every sample used in calibration in practice one will try to find a matrix-matched sample where all analytes are well below the detection limit.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Calibration in Spectroscopy

et al. 1991

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Selectivity and error estimates in multivariate calibration: application to sequential ICP-OES

Cited by 32 publications

References 32 publications

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Comparison of the single channel and multichannel (multivariate) concepts of selectivity in analytical chemistry

Multivariate Calibration in Spectroscopy

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