Variance and Bias Analysis of Information Potential and Symmetric Information Potential

Information theoretical learning (ITL) is a signal processing technique that goes far beyond the traditional techniques based on second order statistics which highly relies on the linearity and Gaussinarity assumptions. Information potential (IP) and symmetric information potential (SIP) are very important concepts in ITL used for system adaptation and data inference. In this paper, a mathematical analysis of the bias and the variance of their estimators is presented. Our results show that the variances decrease as the sample size N increases at the speed of O(N^-1) and a bound exists for the biases. A simple numerical simulation is demonstrated to support our analysis.