Abstract
This paper considers a minimax confidence bound of the normal mean under an asymmetric loss function. A minimax confidence bound is obtained for the case that the variance is known or unknown. The admissibility of the minimax confidence bound is also considered for the case of known variance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berger, J. (1985).Statistical Decision Theory and Bayes Analysis, 2nd ed., Springer-Verlag, New York.
Chen, H. (1966). The optimal minimax character of thet-interval estimation.Kexue Tongbao (Foreign language edition),17, 97–100.
Cohen, A. and Strawderman, W. E. (1973). Admissible confidence interval and point estimation for translation or scale parameters,Annals of Statistics,1, 545–550.
Ferguson, T. S. (1967).Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York.
Joshi, V. M. (1966). Admissibility of confidence intervals,Annals of Mathematical Statistics 37, 629–638.
Kiefer, J. (1957). Invariance, minimax sequential estimation, and continuous time processes,Annals of Mathematical Statistics,28, 573–601.
Lehmann, E. L. (1983).Theory of Point Estimation, Wiley, New York.
Shafie, K. and Noorbalooshi, S. (1995). Asymmetric unbiased estimation in location families,Statistics & Decisions,13, 307–314.
Xiao, Y. (2000). Linear unbiasedness in a prediction problem,Annals of the Institute of Statistical Mathematics,52, 712–721.
Zellner, A. (1986). Bayesian estimation and prediction using asymmetric loss function,Journal of the American Statistical Association,81, 446–451.
Author information
Authors and Affiliations
About this article
Cite this article
Xiao, Y., Takada, Y. & Shi, N. Minimax confidence bound of the normal mean under an asymmetric loss function. Ann Inst Stat Math 57, 167–182 (2005). https://doi.org/10.1007/BF02506886
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02506886