This paper focuses on the problem of a robust estimation of different transformation matrices based on the well known linear discriminant analysis (LDA) as it is used in automatic speech recognition systems. We investigate the effect of class distributions with artificial features and compare the resulting Fisher criterion. This paper shows that it is not very helpful to use only the Fisher criterion for an assessment of class separability. Furthermore we address the problem of dealing with too many additional dimensions in the estimation. Special experiments performed on subsets of the Wallstreet Journal database (WSJ) indicate that a minimum of about 2000 feature vectors per class is needed for robust estimations with monophones. Finally we make a prediction to future experiments on the LDA matrix estimation with more classes.