This paper describes and proposes a method of optimizing the smoothing parameter of an estimator of the probability density function (PDF) called the adaptive kernel estimator (AKE). This optimized estimator is used to build the Bayes classifier in the classification of microarray data. The study profiles and gene expression have made great advances in recent years, thanks to particular to DNA chips. In this field of application, data classification often plays a crucial role. In this regard, different classifiers were used for the diagnosis of cancers from these data such as Bayesian networks, neural networks, support vector machines (SVM) and other classifiers. In this sense, we have proposed a new optimization approach to PDF based on the maximum entropy principle (MEP). The optimized estimation of the probability density is used to improve the quality of the process of classifying data. Experimental results on sets of Microarray data demonstrate that our approach effectively enhances the performance of the classification.