Theory of error for target factor analysis with applications to mass spectrometry and nuclear magnetic resonance spectrometry

Based on the theory of error for abstract factor analysis described earlier, a theory of error for target factor analysis is developed. The theory shows how the error in the data matrix mixes with the error in the target test vector. The apparent error in a target test is found to be a vector sum of the real error in the target vector and the real error in the predicted vector. The theory predicts the magnitudes of these errors without requiring any a priori knowledge of the error in the data matrix or the target vector. A reliability function and a spoil function are developed for the purpose of assessing the validity and the worthi-ness of a target vector. Examples from model data, mass spectrometry and nuclear magnetic -resonance spectrometry are presented.