Abstract
For ap-variate normal mean with known variances, the model proposed by Zellner (1986,J. Amer. Statist. Assoc.,81, 446–451) is discussed in a slightly different framework. A generalized Bayes estimate is derived from a three-stage Bayes point of view under the asymmetric loss function, and the admissibility of such estimators is proved.
Similar content being viewed by others
References
Aitchison, J. and Dunsmore, I. R. (1975).Statistical Prediction Analysis, Cambridge University Press, London.
Berger, J. O. (1985).Statistical Decision Theory: Foundations, Concepts and Methods, Springer, New York.
Blyth, C. R. (1951). On minimax statistical decision procedures and their admissibility,Ann. Math. Statist.,22, 22–42.
Efron, B. and Morris, C. (1973). Stein's estimation rule and its competitors—an empirical Bayes approach,J. Amer. Statist. Assoc.,68, 117–130.
Ferguson, T. S. (1967).Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York.
Lindley, D. V. (1962). Discussion on professor Stein's paper,J. Roy. Statist. Soc. Ser. B,24, 285–287.
Lindley, D. V. (1971a).Foundations of Statistical Inference, 435–455, Holt, Rinehart and Winston, New York.
Lindley, D. V. (1971b).Bayesian Statistics, a Review, SIAM, Philadelphia.
Lindley, D. V. and Smith, A. F. M. (1972). Bayes estimate for the linear model,J. Roy. Statist. Soc. Ser. B,24, 1–41.
Parsian, A. (1989). Bayes estimation using LINEX loss function, (submitted for publication).
Rao, C. R. (1973).Linear Statistical Inference and Its Applications, 2nd ed., Wiley, New York.
Rojo, J. (1987). On the admissibility of\(c\bar x + d\) with respect to the LINEX loss function,Comm. Statist. A—Theory Methods,16, 3745–3748.
Stein, C. (1965).Approximation of Improper Prior Measures by Prior Probability Measures, Bernoulli, Bayes, Laplace Anniversary volume, Springer, New York.
Varian, H. R. (1975). A Bayesian approach to real estate assessment,Studies in Bayesian Econometrics and Statistics in Honour of Leonard J. Savage, (eds. S. E. Fienberg and A. Zellner), 195–208, North-Holland, Amsterdam.
Zellner, A. (1986). Bayesian estimation and prediction using asymmetric loss functions,J. Amer. Statist. Assoc.,81, 446–451.
Author information
Authors and Affiliations
About this article
Cite this article
Parsian, A. On the admissibility of an estimator of a normal mean vector under a linex loss function. Ann Inst Stat Math 42, 657–669 (1990). https://doi.org/10.1007/BF02481143
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02481143