Relation between prediction errors of inverse and classical calibration |
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Authors: | D Grientschnig |
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Institution: | (1) B?hler Edelstahl GmbH & Co KG, Chemical Laboratories, Mariazeller Strasse 25, A-8605 Kapfenberg, Austria, AT |
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Abstract: | The formulae for prediction errors of inverse and classical calibration derived by Centner, Massart and de Jong in the Fresenius’
Journal of Analytical Chemistry (1998) 361 : 2–9 are reconsidered. All calculations assume univariate calibration by ordinary
least squares regression applied to an infinite number of data pairs. Inverse calibration gives rise to an error variance
which is smaller by a certain factor than that of classical calibration. This factor amounts to unity plus the ratio of the
variances of the measurement errors and of the responses used for the calibration. The root mean squared error of prediction
is also smaller for inverse than for classical calibration, namely by the square root of this factor. A prediction error calculated
in that way agrees well with a result obtained by Monte Carlo simulations.
Received: 23 December 1999 / Revised: 14 February 2000 / Accepted: 15 February 2000 |
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