Earticle

The estimation of probability density function (pdf) by the nonparametric kernel methods requires a reliable estimate of the bandwidth. There have been several studies on how to efficiently estimate this parameter. In this work, we propose a new optimization method of the smoothing parameter of the variable kernel estimator (VKE) based on the statistical properties of the probability distributions of random variables. In this setting, we show how to use the maximum entropy principle for estimating the smoothing parameter. The optimized estimator is after used in building the Bayesian classifier. In the same setting, the estimated probability density function is called optimal in the sense of having a minimum error rate of classifying data. Finally, a practical implementation with the aid of a dataset of DNA microarray is used to illustrate the behavior of the optimization technique.