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.
@article{bwmeta1.element.bwnjournal-article-zmv22z3p311bwm, author = {Ryszard Magiera}, title = {Bayes sequential estimation procedures for exponential-type processes}, journal = {Applicationes Mathematicae}, volume = {22}, year = {1994}, pages = {311-320}, zbl = {0812.62086}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p311bwm} }
Magiera, Ryszard. Bayes sequential estimation procedures for exponential-type processes. Applicationes Mathematicae, Tome 22 (1994) pp. 311-320. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p311bwm/
[000] O. E. Barndorff-Nielsen (1980), Conditionality resolutions, Biometrika 67, 293-310. | Zbl 0434.62005
[001] Y. S. Chow, H. Robbins and D. Siegmund (1971), Great Expectations: The Theory of Optimal Stopping, Houghton Mifflin, Boston. | Zbl 0233.60044
[002] E. B. Dynkin (1965), Markov Processes, Vol. 1, Academic Press, New York. | Zbl 0132.37901
[003] G. M. El-Sayyad and P. R. Freeman (1973), Bayesian sequential estimation of a Poisson rate, Biometrika 60, 289-296. | Zbl 0261.62063
[004] R. S. Liptser and A. N. Shiryaev (1978), Statistics of Random Processes, Vol. 2, Springer, Berlin. | Zbl 0556.60003
[005] R. Magiera (1992), Bayes sequential estimation for an exponential family of processes: A discrete time approach, Metrika 39, 1-20. | Zbl 0754.62064
[006] C. N. Morris (1982), Natural exponential families with quadratic variance functions, Ann. Statist. 10, 65-80. | Zbl 0498.62015
[007] B. Novic (1980), Bayes sequential estimation of a Poisson rate: A discrete time approach, ibid. 8, 840-844. | Zbl 0463.62072
[008] S. L. Rasmussen (1980), A Bayesian approach to a problem in sequential estimation, ibid. 8, 1229-1243. | Zbl 0454.62076
[009] 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. | Zbl 0385.62055
[010] 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. | Zbl 0434.62062
[011] C. P. Shapiro and R. L. Wardrop (1980b), Bayesian sequential estimation for one-parameter exponential families, J. Amer. Statist. Assoc. 75, 984-988. | Zbl 0461.62068
[012] A. N. Shiryaev (1973), Statistical Sequential Analysis, Amer. Math. Soc., Providence, R.I.
[013] V. T. Stefanov (1986), Efficient sequential estimation in exponential-type processes, Ann. Statist. 14, 1606-1611. | Zbl 0617.62087
[014] 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.