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Deriving Lehmer and Hölder means as maximum weighted likelihood estimates for the multivariate exponential family
Published 2 May 2024 in math.ST, cs.LG, and stat.TH | (2405.00964v1)
Abstract: The links between the mean families of Lehmer and H\"older 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.
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