Second-order calibration: bilinear least squares regression and a simple alternative

We consider calibration of second-order, or hyphenated instruments generating bilinear two-way data for each specimen. The bilinear regression model is to be estimated from a number of specimens of known composition. We propose a simple estimator and study how it works on real and simulated data. The estimator, which we call the SVD (singular value decomposition) estimator is usually not much less efficient than bilinear least squares. The advantages of our method over bilinear least squares are that it is faster and more easily computed, its standard errors are explicit (and derived in the paper), and it has a simpler correlation structure.