Bilinear Regression and Second Order Calibration

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Linder, Marie,1965-Stockholms universitet,Matematiska institutionen (författare)

Bilinear Regression and Second Order Calibration

BokEngelska1999

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Stockholm :Stockholm University,1999
21 s.
printrdacarrier

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LIBRIS-ID:oai:DiVA.org:su-63156
ISBN:9171538623
https://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-63156URI

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Språk:engelska
Sammanfattning på:engelska

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Härtill 3 uppsatser
We consider calibration of second-order (or "hyphenated") instruments for chemical analysis. Many such instruments generate bilinear two-way (matrix) type data for each specimen. The bilinear regression model is to be estimated from a number of specimens of known composition. Once we have established the regression model from the calibration with specimens of known composition, we can use the model to predict the composition of a new specimen. For the estimation part we propose a new, simple estimator, which we call the SVD (singular value decomposition) estimator, and illustrate how it works on real and simulated data, as compared with other estimation methods, in particular bilinear least squares (BLLS). The SVD estimator is usually only slightly less efficient than BLLS, because it is based on reweighted least squares normal equations. In particular the statistical precision of the SVD estimator and that of BLLS are theoretically investigated, and the methods are compared and illustrated on real and simulated data. The advantages of our method over bilinear least squares are that it is faster and easier to compute, its standard errors are more easily and explicitly obtained, and it has a simpler correlation structure. We also develop a prediction theory based on any of these two estimators. There are numerous alternative estimation/prediction methods in the literature. We give a review of such estimation/prediction methods and carry out an extensive simulation study to compare their estimation and prediction precision. Included in the comparison are BLLS, SVD, GRAM (the generalized rank annihilation method), TLD (the trilinear decomposition method), PARAFAC (parallel factor analysis), PCR (principal components regression) and PLS (partial least squares regression). We conclude that BLLS does best both as estimator and predictor. In some circumstances PARAFAC and TLD do as well as BLLS, but with little information in the calibration set they work badly. Some of the methods do better if they are allowed to predict by a proportional multiple linear regression, whereas other methods do best when they predict with simple proportional regression.

Ämnesord och genrebeteckningar

NATURVETENSKAP Matematik hsv//swe
NATURAL SCIENCES Mathematics hsv//eng
chemometrics
calibration
multivariate
hyphenated methods
matrix data
bilinear model
least squares
singular value decomposition
generalized rank annihilation
trilinear decomposition
parallel factor analysis
principal components regression
partial least squares
prediction
matematisk statistik
Mathematical Statistics

Biuppslag (personer, institutioner, konferenser, titlar ...)

Kroonenberg, Pieter,DrLeiden University (opponent)
Stockholms universitetMatematiska institutionen (creator_code:org_t)

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https://pubs.sub.su.se/4945.pdfPDF (Not accessible to users outside Sweden)
https://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-63156

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Av författaren/redakt...: Linder, Marie, 1 ...; Kroonenberg, Pie ...

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NATURVETENSKAP: NATURVETENSKAP; och Matematik

Av lärosätet: Stockholms universitet

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