Insights into multivariate calibration using errors-in-variables modeling

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A {ital q}-vector of responses, y, is related to a {ital p}-vector of explanatory variables, x, through a causal linear model. In analytical chemistry, y and x might represent the spectrum and associated set of constituent concentrations of a multicomponent sample which are related through Beer`s law. The model parameters are estimated during a calibration process in which both x and y are available for a number of observations (samples/specimens) which are collectively referred to as the calibration set. For new observations, the fitted calibration model is then used as the basis for predicting the unknown values of the new ... continued below

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12 p.

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Thomas, E.V. September 1, 1996.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

A {ital q}-vector of responses, y, is related to a {ital p}-vector of explanatory variables, x, through a causal linear model. In analytical chemistry, y and x might represent the spectrum and associated set of constituent concentrations of a multicomponent sample which are related through Beer`s law. The model parameters are estimated during a calibration process in which both x and y are available for a number of observations (samples/specimens) which are collectively referred to as the calibration set. For new observations, the fitted calibration model is then used as the basis for predicting the unknown values of the new x`s (concentrations) form the associated new y`s (spectra) in the prediction set. This prediction procedure can be viewed as parameter estimation in an errors-in-variables (EIV) framework. In addition to providing a basis for simultaneous inference about the new x`s, consideration of the EIV framework yields a number of insights relating to the design and execution of calibration studies. A particularly interesting result is that predictions of the new x`s for individual samples can be improved by using seemingly unrelated information contained in the y`s from the other members of the prediction set. Furthermore, motivated by this EIV analysis, this result can be extended beyond the causal modeling context to a broader range of applications of multivariate calibration which involve the use of principal components regression.

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12 p.

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OSTI as DE96013406

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  • 2. international workshop on "TLS and errors-in-variables modeling (total leased squares), Leuven (Belgium), 21 Aug 1996

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  • Other: DE96013406
  • Report No.: SAND--96-1973C
  • Report No.: CONF-9608115--1
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 286116
  • Archival Resource Key: ark:/67531/metadc665683

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  • September 1, 1996

Added to The UNT Digital Library

  • June 29, 2015, 9:42 p.m.

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  • April 13, 2016, 2:34 p.m.

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Thomas, E.V. Insights into multivariate calibration using errors-in-variables modeling, article, September 1, 1996; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc665683/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.