Probability density function estimators applied to non-stationary signals

Abstract

This manuscript deals with the estimation of probability density functions. This topic is very important in applied mathematics due to its various applications: Blind identification, blind Separation of Sources, risk theory, game theory, statistical modeling, etc. Since the mid of the 20th century, various solutions have been proposed in order to estimate probability density functions of latent variables and random variables. Hereinafter, a brief survey of major approaches is presented. Meanwhile, we prove that most of proposed methods could be considered as kernel density estimation methods. Theoretical proof for a previously used simulation model is also presented. The application of classic estimators to non-stationary signals is also considered. Finally, simulations are presented and discussed.