Statistics and Its Interface

Volume 17 (2024)

Number 1

Special issue in honor of Professor Lincheng Zhao

Frequentist Bayesian compound inference

Pages: 9 – 26



Jinfeng Xu (City University of Hong Kong)

Ao Yuan (Georgetown University, Washington, District of Columbia, U.S.A.)


In practice often either the Bayesian or frequentist method is used, although there are some combined uses of the two methods, a formal unified methodology of the two hasn’t been seen. Here we first give a brief review of the two methods and some combination of the two, then propose a procedure using both the frequentist likelihood and the Bayesian posterior loss in parameter estimation and hypothesis testing, as an attempt to unify the two methods. Basic properties of the proposed method are studied, and simulation studies are carried out to evaluate the performance of the method.


Bayesian estimate, compound inference, high order behavior, maximum likelihood estimate

2010 Mathematics Subject Classification

62F10, 62F99

Received 17 October 2022

Accepted 10 April 2023

Published 27 November 2023