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Sequential Analysis
Design Methods and Applications
Volume 36, 2017 - Issue 4
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Original Articles

Asymptotically optimal procedures in multivariate Bayesian sequential estimation

Pages 481-489 | Received 15 Aug 2016, Accepted 22 Aug 2017, Published online: 22 Jan 2018

References

  • Arrow, K. J., Blackwell, D., and Girshick, M. A. (1949). Bayes and Minimax Solutions of Sequential Decision Problems, Econometrica 17: 213–244.
  • Bickel, P. J. and Yahav, J. A. (1967). Asymptotically Pointwise Optimal Procedures in Sequential Analysis, in Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, L. M. Le Cam and J. Neyman, eds., pp. 401–413, Berkeley: University of California Press.
  • Bickel, P. J. and Yahav, J. A. (1968). Asymptotically Optimal Bayes and Minimax Procedures in Sequential Estimation, Annals of Mathematical Statistics 33: 442–456.
  • Chow, Y. S., Robbins, H., and Siegmund, D. (1971). Great Expectations: The Theory of Optimal Stopping, Boston: Houghton Mifflin.
  • Chow, Y. S. and Yu, K. F. (1981). On the Performance of a Sequential Procedure for the Estimation of the Mean, Annals of Statistics 9: 184–189.
  • Ghosh, B. K. and Sen, P. K. (1991). Handbook of Sequential Analysis, edited volume, New York: Dekker.
  • Ghosh, M. and Hoekstra, R. M. (1989). A.P.O. Rules in Hierarchical and Empirical Bayes Models, Sequential Analysis 8: 79–100.
  • Ghosh, M. and Hoekstra, R. M. (1995). A.P.O. Rules in Hierarchical Bayes Regression Models, Sequential Analysis 14: 99–115.
  • Ghosh, M., Mukhopadhyay, N., and Sen, P. K. (1997). Sequential Estimation, New York: Wiley.
  • Ghosh, M., Sinha, B. K., and Mukhopadhyay, N. (1976). Multivariate Sequential Point Estimation, Journal of Multivariate Analysis 6: 281–294.
  • Hwang, L.-C. (1999). A Robust Asymptotically Optimal Procedure in Bayes Sequential Estimation, Statistica Sinica 9: 893–904.
  • Hwang, L.-C. (2001). Asymptotically Pointwise Optimal Rules in the Poisson Process, Sequential Analysis 20: 13–23.
  • Hwang, L.-C. and Lee, C.-H. (2012). Bayes Sequential Estimation for One-Parameter Exponential Family under Asymmetric LINEX Loss Function, Sequential Analysis 31: 3–21.
  • Martinsek, A. T. (1987). Empirical Bayes Methods in Sequential Estimation, Sequential Analysis 6: 119–137.
  • Sen, P. K. and Ghosh, M. (1981). Sequential Point Estimation of Estimable Parameters Based on U-Statistics, Sankhyā, Series A 43: 331–344.
  • Takada, Y. (2001). Bayes Sequential Estimation of Poisson Mean under a Linex Loss Function, Sequential Analysis 20: 55–64.
  • Takada, Y. and Nagao, H. (2004). Asymptotic Improvement of the Sample Mean Vector for Sequential Point Estimation of a Multivariate Normal Mean with a LINEX Loss Function, Scientiae Mathematicae Japonicae 60: 337–345.
  • Wald, A. (1951). Asymptotic Minimax Solutions of Sequential Point Estimation Problems, in Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman, ed., pp. 1–11, Los Angeles: University of California Press.
  • Woodroofe, M. (1981). A.P.O. Rules are Asymptotically Non-Deficient for Estimation with Squared Error Loss, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 58: 331–341.

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