Institute of Mathematical Statistics Collections

Multiagent estimators of an exponential mean

Constance van Eeden and James V. Zidek

Full-text: Open access

Abstract

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.

Chapter information

Source
Dominique Fourdrinier, Éric Marchand and Andrew L. Rukhin, eds., Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2012), 131-153

Dates
First available in Project Euclid: 14 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1331731617

Digital Object Identifier
doi:10.1214/11-IMSCOLL810

Mathematical Reviews number (MathSciNet)
MR3202508

Zentralblatt MATH identifier
1326.62019

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures 62C15: Admissibility
Secondary: 62F10: Point estimation

Keywords
conjugate utility exponential–mean estimation forecasting G–admissibility multiagent decision theory Pareto optimality

Rights
Copyright © 2012, Institute of Mathematical Statistics

Citation

van Eeden, Constance; Zidek, James V. Multiagent estimators of an exponential mean. Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman, 131--153, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2012. doi:10.1214/11-IMSCOLL810. https://projecteuclid.org/euclid.imsc/1331731617


Export citation

References

  • Akaike, H. (1977). On entropy maximization principle. In: Applications of statistics, Proceedings of the symposium held at Wright State University, Dayton, Ohio, 14–18 June 1976. (P.R. Krishnaiah, Editor), Elsevier, North-Holland, 27–41.
  • Akaike, H. (1981). Likelihood of a model and information criteria. J. Econometrics, 16, 3–14.
  • Al-Hussaini, E.K. and Ahmed, A.E.A. (2003). On Bayesian interval prediction of future records. Test, 12, 79–99.
  • Geisser, S. (1985). Interval prediction for Pareto and exponential observables. J. Econometrics, 29, 173–185.
  • Geisser, S. (1993). Predictive inference: An introduction. London: Chapman and Hall.
  • Genest, C. and Zidek, J.V. (1986). Combining probability distributions: a critique and an annotated bibliography. Statist. Sci., 1, 114–148.
  • Haines, L.M. (2003). An approach to simple bargaining games and related problems. J. Statist. Plann. Inference, 116, 353–366.
  • Lindley, D.V. (1976). A class of utility functions. Ann. Statist., 4, 1–10.
  • Parsons, S. and Wooldridge, M. (2002). Game theory and decision theory in multi-agent systems. Autonomous Agents and Multi-Agent Systems, 5, 243–254.
  • Radner, R. (1962). Team decision problems. Ann. Math. Statist., 33, 857–881.
  • Tobías, A. and Scotto, M.G. (2005). Prediction of extreme ozone levels in Barcelona, Spain. Environmental Monitoring and Assessment, 100, 23–32.
  • van Eeden, C. and Zidek, J.V. (1994). Group Bayes estimation of the exponential mean: A retrospective view of the Wald theory. In: Statistical Decision Theory and Related Topics V (S.S. Gupta and J.O. Berger, eds.), Springer–Verlag, 35–49.
  • van Eeden, C. and Zidek, J.V. (2005). Multi-agent predictors of an exponential interevent time. Tech. Report Nr. 215, Department of Statistics, University of British Columbia, Vancouver, Canada.
  • Weerhandi, S. and Zidek, J.V. (1983). Elements of multi-Bayesian decision theory, Ann. Statist., 11, 1032–1046.