Multivariate calibration of non-replicated measurements for heteroscedastic errors

Multivariate calibration of non-replicated measurements for the factored noise model

The accuracy of a multivariate calibration (MVC) model for relating concentrations of multicomponent mixtures to their spectral measurements, depends on effective handling of errors in the measured data. For the case when error variances vary along only one mode (either along mixtures or along wavelengths), a method to estimate the error variances simultaneously along with the spectral subspace...

Modeling of Heteroscedastic Measurement Errors

On Estimation Problem in Multivariate Linear Calibration with Elliptical Errors

The estimation problem in multivariate linear calibration with elliptical errors is considered under a loss function which can be derived from the Kullback-Leibler distance. First, we discuss the problem under normal errors and we give unbiased estimate of risk of an alternative estimator by means of the Stein and Stein-Haff identities for multivariate normal distribution. From the unbiased est...

Bagging for robust non-linear multivariate calibration of spectroscopy

This paper presents the application of the bagging technique for non-linear regression models to obtain more accurate and robust calibration of spectroscopy. Bagging refers to the combination of multiple models obtained by bootstrap re-sampling with replacement into an ensemble model to reduce prediction errors. It is well suited to “non-robust” models, such as the non-linear calibration method...

Extent-based kinetic identification using spectroscopic measurements and multivariate calibration.

Extent-based kinetic identification is a kinetic modeling technique that uses concentration measurements to compute extents and identify reaction kinetics by the integral method of parameter estimation. This article considers the case where spectroscopic data are used together with a calibration model to predict concentrations. The calibration set is assumed to be constructed from reacting data...