Deriving Generalized Means as Least Squares and Maximum Likelihood Estimates

Functions called generalized means are of interest in statistics because they are simple to compute, have intuitive appeal, and can serve as reasonable parameter estimates.The well-known arithmetic, geometric, and harmonic means are all examples of generalized means.We show how generalized means can be derived in a unified way, as least squares estimates for a transformed data set.We also investigate models that have generalized means as their maximum likelihood estimates.