Centrality Estimators for Probability Density Functions
This work offers a theoretical extension for density estimation in statistics and machine learning, though it appears incremental as it generalizes existing maximum likelihood approaches.
The authors introduced a family of centrality estimators for probability density function fitting, showing that maximum likelihood is a special case and providing a new probability interpretation of Fisher maximum likelihood. They demonstrated the effectiveness of Hölder and Lehmer estimators through numerical simulations.
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 Hölder 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.