Multiagent estimators of an exponential mean. (English) Zbl 1326.62019

van Eeden, Constance; Zidek, James V.

Fourdrinier, Dominique (ed.) et al., Contemporary developments in Bayesian analysis and statistical decision theory. A festschrift for William E. Strawderman. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-81-2). Institute of Mathematical Statistics Collections 8, 131-153 (2012).

Summary: Some Bayesian agents must produce a joint estimator of the mean of an exponentially distributed random variable \(S\) from a sample of realizations \(S\). Their priors may differ but they have the same utility function. For the case of two agents, the Pareto efficient boundary of the utility set generated by the class of all non-randomized linear estimation rules is explored in this paper. Conditions are given that make those rules \(G\)-complete within the class of non-randomized linear estimators, meaning that optimum non-random estimators can be found on the Pareto boundary thereby providing a basis for a meaningful consensus.
For the entire collection see [Zbl 1319.62003].

MSC:

62C10	Bayesian problems; characterization of Bayes procedures
62C15	Admissibility in statistical decision theory
62F10	Point estimation

Keywords:

conjugate utility; exponential-mean estimation; forecasting; G-admissibility; multiagent decision theory; Pareto optimality