Estimation and Calibration for Multivariate Linear Models with Errors in Variables

• Activity Number: 315
• Type: Invited
• Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Bernd Wolfgang Igl*+ and Lutz Duembgen
• Companies: University of Luebeck and University of Berne
• Keywords: errors-in-variables ; calibration ; multivariate linear regression model ; total least squares ; correction for attenuation

Abstract

This work is motivated by calibration problems in analytical chemistry. Precisely, $p$ different gas sensors are used to determine the concentrations of $r$ gas components in a mixture. Denoting the vector of true sensor signals with $\eta$, we assume a linear dependency on the vector $\xi$ of true gas concentrations. However, in the calibration phase both variables are subject to error, which leads to an errors-in-variables setting. That means, $x$ is an erroneous measurement of an unobservable true parameter vector $\xi$. Similarly, $y$ is a noise corrupted observation of $\eta$. The main aim is to predict a future value $\xi_o$ of true gas concentrations based on a measured vector of noisy signals $y_o$.

In order to estimate the underlying regression parameters relating $\eta$ to $\xi$, ordinary least squares estimates are inadequate. In the present talk, two estimation techniques are compared: `total-least-squares' and `LS with correction for attenuation' due to Gleser (JASA, 1992). Starting from such estimators in the calibration phase we propose a prediction region for a future parameter $\xi_o$ which is based on a certain bootstrap method.