Improved Estimation of Poisson Menas under Balanced Loss Function

  • Published : 2000.12.01


Zellner(1994) introduced the notion of a balanced loss function in the context of a general liner model to reflect both goodness of fit and precision of estimation. We study the perspective of unifying a variety of results both frequentist and Bayesian from Poisson distributions. We show that frequentist and Bayesian results for balanced loss follow from and also imply related results for quadratic loss functions reflecting only precision of estimation. Several examples are given for Poisson distribution.


  1. Communications in Statistics-Theory and Methods v.26 Simultaneous estimation of the multivariate normal mean under balanced loss function Chung, Y.;Kim, C.
  2. Far East Journal of Theoretical Statistics v.2 Minimax estimation of multivariate normal mean under balanced loss function Chung, Y.;Kim, C.
  3. Statistics and Decisions v.17 A new class of minimax estimator of multivariate normal mean vector under balanced loss function Chung, Y.;Kim, C.;Dey, D.K.
  4. Statistics and Decisions v.16 Linear estimators of Poisson mean under balanced loss functions Chung, Y.;Kim, C.;Song, S.
  5. Annals of Statistics v.11 Construction of improved estimators in multiparameter estimation for discrete esponential families Ghosh, M.;Hwang, J.T.;Tsui, K.W.
  6. Annals of Statistics v.6 A natural identity for exponential families with applications in multi-parameter estimation Hudson, H.M.
  7. Annals of Statistics v.10 Improving upon standard estimators in discrete exponential families with application to Poisson and negative binomial laws Hwang, J.T.
  8. Communication in Statistics - Theory and Methods v.23 Weighted balanced loss function for the exponential time to failure Rodrigue, J.;Zellner, A.
  9. Sanhkaya A. Unbiased minimum variance estimation in a class of discrete distribution Roy, J.;Mitra, S.K.
  10. Statistical decision Theory and Related Topics V Bayesian and non-Bayesian estimation using balanced loss function Zellner, A.;J.O. Berger(ed.);S.S. Gupta(ed.)