EXACT MEAN SQUARED ERROR COMPARISONS OF THE INVERSE AND CLASSICAL ESTIMATORS IN MULTI-UNIVARIATE LINEAR CALIBRATION

The problem of controlled linear calibration with a multivariate respo nse and univariate explanatory variable is considered. Exact expressio ns (in terms of functions of Poisson variables) are derived for the me an squared error of the inverse estimator. These expressions are compa red with ones previously derived for the mean squared error of the cla ssical estimator. Previous comparisons between the two estimators have suggested that neither dominates the other. We prove that this is tru e, and provide numerical comparisons of the two estimators' risk funct ions.