×

zbMATH — the first resource for mathematics

Empirical Bayes sequential estimation of the mean. (English) Zbl 0746.62082
Summary: We consider the empirical Bayes problem where the component problem is the sequential estimation of the mean of a distribution with squared error decision loss plus a sampling cost. An empirical Bayes sequential estimation procedure is exhibited which is asymptotically optimal. Asymptotic efficiency of the empirical Bayes stopping time sequence is also established. The performance of the proposed empirical Bayes procedure is studied with the help of a Monte Carlo study.

MSC:
62L12 Sequential estimation
62C12 Empirical decision procedures; empirical Bayes procedures
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chow Y.S., Great Expectations: The Theory of Optimal Stopping (1971) · Zbl 0233.60044
[2] Erickson W.A., J. Roy. Statist Soc 31 pp 195– (1969)
[3] DOI: 10.2307/2284155 · Zbl 0275.62005 · doi:10.2307/2284155
[4] Ferguson T.S., A Decision Theoretical Approach (1967)
[5] DOI: 10.2307/2289083 · Zbl 0616.62012 · doi:10.2307/2289083
[6] DOI: 10.2307/2289394 · doi:10.2307/2289394
[7] DOI: 10.1080/07474948908836168 · Zbl 0681.62066 · doi:10.1080/07474948908836168
[8] DOI: 10.1007/BF00053965 · Zbl 0681.62013 · doi:10.1007/BF00053965
[9] Hartigan J.A., J. Roy. Statist Soc. 40 pp 446– (1969)
[10] DOI: 10.1214/aos/1176350961 · Zbl 0725.62011 · doi:10.1214/aos/1176350961
[11] DOI: 10.1080/03610928908830049 · Zbl 0696.62340 · doi:10.1080/03610928908830049
[12] Karunamuni R.J., To appear in Ann. Inst Statist Math. 42 (1990)
[13] Laippala P., Scani. J. Statist. 6 pp 113– (1979)
[14] DOI: 10.1007/BF02481100 · Zbl 0583.62008 · doi:10.1007/BF02481100
[15] Maritz J.S., Empirical Bayes Methods (1979) · Zbl 0245.62001
[16] DOI: 10.1080/07474948708836120 · Zbl 0628.62081 · doi:10.1080/07474948708836120
[17] DOI: 10.2307/2287098 · Zbl 0506.62005 · doi:10.2307/2287098
[18] Robbins, H. An empirical Bayes approach to statistics. Proc. Third Berkeley Symp. Math. Statist Prob. Vol. 1, pp.157–163. Univ. of California Press.
[19] Robbins H., Probability and Statistics (1959)
[20] DOI: 10.2307/1401373 · Zbl 0117.14104 · doi:10.2307/1401373
[21] DOI: 10.1214/aoms/1177703729 · Zbl 0138.12304 · doi:10.1214/aoms/1177703729
[22] Sen P.K., Sequential Nonparametrics (1981) · Zbl 0583.62074
[23] Susarla V., Encyclopedia of Statistical Science 2 pp 490– (1982)
[24] Woodroofe, M. Nonlinear Renewal Theory in Sequential Analysis. CBMS-NDF Regional Conference Series in Applied Mathematics. · Zbl 0487.62062
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.