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The validity of a classifier depends on the precision of the error estimator used to estimate its true error. This paper considers the necessary sample size to achieve a given validity measure, namely RMS, for resubstitution and leave-one-out error estimators in the context of LDA. It provides bounds for the RMS between the true error and both the resubstitution and leave-one-out error estimators in terms of sample size and dimensionality. These bounds can be used to determine the minimum sample size in order to obtain a desired estimation accuracy, relative to RMS. To show how these results can be used in practice, a microarray classification problem is presented.