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The use of k nearest neighbor (k-NN) and Parzen density estimates to obtain estimates of the Bayes error is investigated under limited design set conditions. By drawing analogies between the k-NN and Parzen procedures, new procedures are suggested, and experimental results are given which indicate that these procedures yield a significant improvement over the conventional k-NN and Parzen procedures. We show that, by varying the decision threshold, many of the biases associated with the k-NN or Parzen density estimates may be compensated, and successful error estimation may be performed in spite of these biases. Experimental results are given which demonstrate the effect of kernel size and shape (Parzen), the size of k (k-NN), and the number of samples in the design set.