Random calibration with many measurements: An application of stein estimation

Samuel D. Oman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In the problem considered, a vector of many imprecise measurements (e.g., spectroscopic) is used to linearly predict a quantity whose precise measurement is difficult or expensive. The regression vector is estimated from a calibration experiment having both types of measurements for a random sample. Most previous approaches to this problem adjust for approximate multicollinearity, which often results from the correlations among the imprecise measurements, by inverting an approximation (e.g., factor-analytic) to their covariance matrix. In the approach here, it is argued that the regression vector should lie in a lower dimensional suhspace determined by the principal components of the covariance matrix. It is then estimated by applying a Stein contraction of the least squares estimator to the principal components regression estimator. Examples using real data are presented in which the proposed estimator substantially improves on the ordinary least squares estimation.

Original languageEnglish
Pages (from-to)187-195
Number of pages9
JournalTechnometrics
Volume33
Issue number2
DOIs
StatePublished - May 1991

Keywords

  • Prediction
  • Pretest estimator
  • Principal components regression
  • Spectrometer measurements

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