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A method to reduce the mean integrated squared error for kernel distribution function estimators is proposed. It can be shown that the asymptotic bias of the proposed method is considerably smaller in... the sense of convergence rate than that of the standard kernel distribution function estimator. Even though the rate of convergence of variance does not change, the variance of our proposed method is smaller up to some constants. The idea of this method is using a self-elimination technique between two standard kernel distribution function estimators with different bandwidths, with some helps of exponential and logarithmic expansions. By doing that, vanishing the first term of the asymptotic bias is possible. As a result, mean squared error can be reduced.show more
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