The error-entropy-minimization approach in adaptive system training is addressed in this paper. The effect of Parzen windowing on the location of the global minimum of entropy has been investigated. An analytical proof that shows the global minimum of the entropy is a local minimum, possibly the global minimum, of the nonparametrically estimated entropy using Parzen windowing with Gaussian kernels. The performances of error-entropy-minimization and the mean-square-errorminimization criteria are compared in short-term prediction of a chaotic time series. Statistical behavior of the estimation errors and the higher order central moments of the time series data and its predictions are utilized as the comparison criteria.