Centrality Estimators for Probability Density Functions
Djemel Ziou
In this report, we explore the data selection leading to a family of
estimators maximizing a centrality. The family allows a nice properties leading
to accurate and robust probability density function fitting according to some
criteria we define. We establish a link between the centrality estimator and
the maximum likelihood, showing that the latter is a particular case.
Therefore, a new probability interpretation of Fisher maximum likelihood is
provided. We will introduce and study two specific centralities that we have
named H\"older and Lehmer estimators. A numerical simulation is provided
showing the effectiveness of the proposed families of estimators opening the
door to development of new concepts and algorithms in machine learning, data
mining, statistics, and data analysis.