Large Sample Estimation and Higher Order Efficiency: Bayesian, Likelihood and Frequentist

Abstract

In this manuscript, the consistency, asymptotic efficiency and exponential rate of convergence of Bayes estimator, maximum likelihood estimator and probability ratio estimator have been discussed and studied. It shows that the maximum likelihood estimator is an approximation for the probability ratio estimator. Further, it also shows that the probability ratio estimator is superior than Bayes estimator and maximum likelihood estimator in exponential rate of convergence. Several examples are provided to support the claim.