Marginal Maximum Likelihood Estimators for Ranked Means in Exponential Families

摘要

In this article, we study the estimation of the smallest or the largest parameters of p exponential populations. The marginal MLE of the smaller and the larger of two population means in an exponential family can be obtained by solving an equation. The case of general p is also discussed. An iteration formula for solving a marginal MLE is proposed. Asymptotic properties of the marginal MLE have also been studied.rnSome Monte-Carlo simulations for Poisson model have been studied. The numerical results support the superiority of the marginal MLE against that of the usual MLE in the sense of biasedness and mean square error.