Abstract
We construct the empirical Bayes (EB)estimation of the parameter in two-side truncated distribution families with asymmetric Linex loss using negatively associated (NA) samples. The asymptotical optimality and convergence rate of the EB estimation is obtained. We will show that the convergence rate can be arbitrarily close toO(n −q),q=λs(δ−2)/δ(s+2).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. P. Basu and N. Ebrahimi,Bayesian approach to life testing and reliability estimation using asymmetric loss function, J. Statist. Plann. Inference29 (1991), 21–31.
S. Y. Huang,Empirical Bayes testing procedures in some nonexponential families using asymmetric Linex Loss function, J. Statist. Plann. Inference46 (1995), 293–309.
S. Y. Huang and T. C. Liang,Empirical Bayes estimation of the truncation parameter with Linex loss, Statistica Sinica7 (1997), 755–769.
H. Liang,The convergence of estimation for two-dimension two-sided truncated distribution families, Mathematical Statistics and Applied Probability,4 (1991), 433–447.
Shi, Yimin,Empirical Bayes estimation for parameter of two-sided truncated distribution under Linex loss function, Appl. Math. J. Chinese Univ. Ser A,4 (2000), 475–483.
Su Chun, etc,Moment inequalities and weak convergence for negatively associated sequences, Sciences in China (Series A)12 (1996), 1091–1099.
H. R. Varian,A Bayesian approach to real estate assessment, In Studies in Bayesian Econometrics and Statistics in Honor of L. J. Savage (Edited by S.E. Feinberg and A. Zellner), North-Holland, Amsterdam, (1975), 195–208.
L. S. Wei,The empirical Bayes test problem for scale exponential family: in the case of NA samples, Acta Mathematical Appl. Sinica3 (2000), 403–412
Younshik Chung,Estimation of scale parameter from Rayleigh distribution under entropy loss, J. Appl. Math. & Computing (old KJCAM)1 (1995), 33–40.
Younshik ChungSimultaneous estimation of gamma scale parameter under entropy loss: Bayesian approach, J. Appl. Math. & Computing (old KJCAM)1 (1996), 55–64.
A. Zellner,Bayesian estimation and prediction using asymmetric Loss functions, J. Amer. Statist. Assoc.81 (1986), 446–451.
L. C. Zhao,Convergence Rate of empirical Bayes estimation for parameters of a discrete distributed family, Journal of Mathematical Research and Exposition1 (1981), 59–69.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the Natural Science Foundation of the Education Department of Shaanxi Province (No. 03JK065)
Yimin Shi received his M. Sc in statistics from Northwestern Polytechnical University (NPU). He is a professor in applied Mathematics at NPU, his research interests include applied probability statistics, Reliability theory, Bayes analysis and inference.
Xiaolin Shi is a graduated student at NPU. Her research interests focus on signal processing, computer simulation.
Shesheng Gao received his M. Sc in 1993 and doctor degress in 1999 from NPU. He is a associate professor in automatic school at NPU. His research interests focus on control theory and control enginneering, intelligence information fusion theory and application.
Rights and permissions
About this article
Cite this article
Shi, Y., Shi, X. & Gao, S. Empirical Bayes estimation of the truncation parameter with asymmetric loss function using NA samples. JAMC 14, 305–317 (2004). https://doi.org/10.1007/BF02936116
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02936116