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Using maximum weighted likelihood to derive Lehmer and Hölder mean families
Djemel Ziou · 2023-05-28 · via math.ST updates on arXiv.org

In this paper, we establish the links between the Lehmer and Hölder 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 Hölder 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.

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