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In the discrimination problem the random variable , known to take values in , is estimated from the random vector . All that is known about the joint distribution of is that which can be inferred from a sample of size drawn from that distribution. A discrimination nde is any procedure which determines a decision for from and . For rules which are determined by potential functions it is shown that the mean-square difference between the probability of error for the nde and its deleted estimate is bounded by where is an explicitly given constant depending only on and the potential function. The behavior is shown to be the best possible for one of the most commonly encountered rules of this type.