The Bhattacharyya Bound is a measurement of the error rate of a classifier. If the distributions of the classes are independent Normal distributions, and their parameters are known, the Bhattacharyya Bound can be calculated explicitly. On the other hand, if the parameters of the distributions are unknown this bound has to be estimated. Both the theory and simulation results indicate that the estimator of the Bhattacharyya Bound given by traditional methods is seriously biased especially when the training sample size is small. By applying the bootstrap technique to the problem of estimating the Bhattacharyya Bound, we introduce several bootstrap schemes for this purpose. The results of the simulations prove that the bootstrap technique works very successfully, and dramatically reduces the bias of the estimate.

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Oommen, J, & Wang, Q. (Qun). (2001). Computing the Bhattacharyya error bound in classifiers using direct bias correction bootstrap methods. Advances in Neural Networks and Applications, 70–76.