Using maximum weighted likelihood to derive Lehmer and Hölder mean families

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.