Deriving Lehmer and Hölder means as maximum weighted likelihood estimates for the multivariate exponential family
This work offers a theoretical extension for statistical methods, but it is incremental as it builds directly on prior univariate results.
The authors extended the connection between Lehmer and Hölder means and weighted maximum likelihood estimators from univariate to multivariate exponential families, providing a probabilistic interpretation that could enhance their applications.
The links between the mean families of Lehmer and Hölder and the weighted maximum likelihood estimator have recently been established in the case of a regular univariate exponential family. In this article, we will extend the outcomes obtained to the multivariate case. This extension provides a probabilistic interpretation of these families of means and could therefore broaden their uses in various applications.