GENERALIZED RANK ANNIHILATION METHOD .2. BIAS AND VARIANCE IN THE ESTIMATED EIGENVALUES

Rank annihilation factor analysis (RAFA) is a method for multicomponen t calibration using two data matrices simultaneously, one for the unkn own and one for the calibration sample. In its most general form, the generalized rank annihilation method (GRAM), an eigenvalue problem has to be solved. In this second paper expressions are derived for predic ting the bias and variance in the eigenvalues of GRAM. These expressio ns are built on the analogies between a reformulation of the eigenvalu e problem and the prediction equations of univariate and multivariate calibration. The error analysis will also be performed for Lorber's fo rmulation of RAFA. It will be demonstrated that, depending on the size of the eigenvalue, large differences in performance must be expected. A bias correction technique is proposed that effectively eliminates t he bias if the error in the bias estimate is not too large. The derive d expressions are evaluated by Monte Carlo simulations. It is shown th at the predictions are satisfactory up to the limit of detection. The results are not sensitive to an incorrect choice of the dimension of t he factor space.