Using maximum weighted likelihood to derive Lehmer and H\"older mean families
Other Statistics
2023-12-21 v2 Statistics Theory
Statistics Theory
Abstract
In this paper, we establish the links between the Lehmer and H\"older mean families and maximum weighted likelihood estimator. Considering the regular one-parameter exponential family of probability density functions, we show that the maximum weighted likelihood of the parameter is a generalized weighted mean family from which Lehmer and H\"older mean families are derived. Some of the outcomes obtained provide a probabilistic interpretation of these mean families and could therefore broaden their uses in various applications.
Keywords
Cite
@article{arxiv.2305.18366,
title = {Using maximum weighted likelihood to derive Lehmer and H\"older mean families},
author = {Djemel Ziou},
journal= {arXiv preprint arXiv:2305.18366},
year = {2023}
}