# Bayes sequential estimation procedures for exponential-type processes

Applicationes Mathematicae (1994)

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

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topMagiera, 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

top- O. E. Barndorff-Nielsen (1980), Conditionality resolutions, Biometrika 67, 293-310. Zbl0434.62005
- Y. S. Chow, H. Robbins and D. Siegmund (1971), Great Expectations: The Theory of Optimal Stopping, Houghton Mifflin, Boston. Zbl0233.60044
- E. B. Dynkin (1965), Markov Processes, Vol. 1, Academic Press, New York. Zbl0132.37901
- G. M. El-Sayyad and P. R. Freeman (1973), Bayesian sequential estimation of a Poisson rate, Biometrika 60, 289-296. Zbl0261.62063
- R. S. Liptser and A. N. Shiryaev (1978), Statistics of Random Processes, Vol. 2, Springer, Berlin. Zbl0556.60003
- R. Magiera (1992), Bayes sequential estimation for an exponential family of processes: A discrete time approach, Metrika 39, 1-20. Zbl0754.62064
- C. N. Morris (1982), Natural exponential families with quadratic variance functions, Ann. Statist. 10, 65-80. Zbl0498.62015
- B. Novic (1980), Bayes sequential estimation of a Poisson rate: A discrete time approach, ibid. 8, 840-844. Zbl0463.62072
- S. L. Rasmussen (1980), A Bayesian approach to a problem in sequential estimation, ibid. 8, 1229-1243. Zbl0454.62076
- 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
- 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
- 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
- A. N. Shiryaev (1973), Statistical Sequential Analysis, Amer. Math. Soc., Providence, R.I.
- V. T. Stefanov (1986), Efficient sequential estimation in exponential-type processes, Ann. Statist. 14, 1606-1611. Zbl0617.62087
- 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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