Sd. Oman et Ms. Srivastava, EXACT MEAN SQUARED ERROR COMPARISONS OF THE INVERSE AND CLASSICAL ESTIMATORS IN MULTI-UNIVARIATE LINEAR CALIBRATION, Scandinavian journal of statistics, 23(4), 1996, pp. 473-488
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.