Bayes sequential estimation procedures for exponential-type processes

Ryszard Magiera

Applicationes Mathematicae (1994)

  • Volume: 22, Issue: 3, page 311-320
  • ISSN: 1233-7234

Abstract

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The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.

How to cite

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Magiera, Ryszard. "Bayes sequential estimation procedures for exponential-type processes." Applicationes Mathematicae 22.3 (1994): 311-320. <http://eudml.org/doc/219097>.

@article{Magiera1994,
abstract = {The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.},
author = {Magiera, Ryszard},
journal = {Applicationes Mathematicae},
keywords = {Bayes sequential estimation; exponential-type process; stopping time; sequential decision procedure; exponential family of processes; Bayesian sequential estimation; continuous time stochastic processes; mean},
language = {eng},
number = {3},
pages = {311-320},
title = {Bayes sequential estimation procedures for exponential-type processes},
url = {http://eudml.org/doc/219097},
volume = {22},
year = {1994},
}

TY - JOUR
AU - Magiera, Ryszard
TI - Bayes sequential estimation procedures for exponential-type processes
JO - Applicationes Mathematicae
PY - 1994
VL - 22
IS - 3
SP - 311
EP - 320
AB - The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.
LA - eng
KW - Bayes sequential estimation; exponential-type process; stopping time; sequential decision procedure; exponential family of processes; Bayesian sequential estimation; continuous time stochastic processes; mean
UR - http://eudml.org/doc/219097
ER -

References

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  1. O. E. Barndorff-Nielsen (1980), Conditionality resolutions, Biometrika 67, 293-310. Zbl0434.62005
  2. Y. S. Chow, H. Robbins and D. Siegmund (1971), Great Expectations: The Theory of Optimal Stopping, Houghton Mifflin, Boston. Zbl0233.60044
  3. E. B. Dynkin (1965), Markov Processes, Vol. 1, Academic Press, New York. Zbl0132.37901
  4. G. M. El-Sayyad and P. R. Freeman (1973), Bayesian sequential estimation of a Poisson rate, Biometrika 60, 289-296. Zbl0261.62063
  5. R. S. Liptser and A. N. Shiryaev (1978), Statistics of Random Processes, Vol. 2, Springer, Berlin. Zbl0556.60003
  6. R. Magiera (1992), Bayes sequential estimation for an exponential family of processes: A discrete time approach, Metrika 39, 1-20. Zbl0754.62064
  7. C. N. Morris (1982), Natural exponential families with quadratic variance functions, Ann. Statist. 10, 65-80. Zbl0498.62015
  8. B. Novic (1980), Bayes sequential estimation of a Poisson rate: A discrete time approach, ibid. 8, 840-844. Zbl0463.62072
  9. S. L. Rasmussen (1980), A Bayesian approach to a problem in sequential estimation, ibid. 8, 1229-1243. Zbl0454.62076
  10. C. P. Shapiro and R. L. Wardrop (1978), The Bayes sequential procedure for estimating the arrival rate of a Poisson process, J. Amer. Statist. Assoc. 73, 597-601. Zbl0385.62055
  11. C. P. Shapiro and R. L. Wardrop (1980a), Dynkin's identity applied to Bayes sequential estimation of a Poisson process rate, Ann. Statist. 8, 171-182. Zbl0434.62062
  12. C. P. Shapiro and R. L. Wardrop (1980b), Bayesian sequential estimation for one-parameter exponential families, J. Amer. Statist. Assoc. 75, 984-988. Zbl0461.62068
  13. A. N. Shiryaev (1973), Statistical Sequential Analysis, Amer. Math. Soc., Providence, R.I. 
  14. V. T. Stefanov (1986), Efficient sequential estimation in exponential-type processes, Ann. Statist. 14, 1606-1611. Zbl0617.62087
  15. V. T. Stefanov (1988), A sequential approach for reducing curved exponential families of stochastic processes to noncurved exponential ones, in: Contemp. Math. 80, Amer. Math. Soc., 323-330. 

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