×

zbMATH — the first resource for mathematics

Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean. (English) Zbl 0144.41405

Keywords:
statistics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] D. Blackweli, and M. A. Girshick, Theory of Games and Statistical Decisions, John Wiley and Sons, New York, 1954. · Zbl 0056.36303
[2] M. A. Girshick, and L. J. Savage, ”Bayes and minimax estimates for quadratic loss functions,” Second Berkeley Symposium on Mathematical Statistics and Probability, University of California, Berkeley, 1951, 53–73. · Zbl 0045.41002
[3] J. L. Hodges, Jr., and E. L. Lehmann, ”Some applications of the CramĂ©r-Rao inequality,” Second Berkeley Symposium on Mathematical Statistics and Probability, University of California, Berkeley, 1951, 13–22.
[4] W. James, and C. Stein, ”Estimation with quadratic loss,” Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California, Berkeley, I (1961), 361–379. · Zbl 1281.62026
[5] J. Kiefer, ”Invariance minimax sequential estimation and continuous time processes,” Ann. Math. Statist., 28 (1957), 573–601. · Zbl 0080.13004 · doi:10.1214/aoms/1177706874
[6] H. Kudo, ”On minimax invariant estimators of the transformation parameter,” Nat. Sci. Rep. Ochanomizu Univ., 6 (1955), 31–73. · Zbl 0066.38601
[7] H. B. Mann, Analysis and Design of Experiments, Dover Publications, New York, 1949. · Zbl 0033.02803
[8] H. Robbins, ”Asymptotically subminimax solutions of compound statistical decision problems,” Second Berkeley Symposium on Mathematical Statistics and Probability, University of California, Berkeley, 1951, 131–148. · Zbl 0044.14803
[9] C. Stein, ”Multiple regression,” Contributions to Probability and Statistics Essays in Honor of Harold Hotelling, Stanford, 1960, 424–443.
[10] [10] M. Stone, ”The posterior t-distribution,” Ann. Math. Statist., 34 (1963) 568–573. · Zbl 0115.36503 · doi:10.1214/aoms/1177704169
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.