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Biased versus unbiased estimation. (English) Zbl 0306.62010

MSC:
62F10Point estimation
62C15Statistical admissibility
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Full Text: DOI
References:
[1] Anderson, T. W.: The statistical analysis of time series. (1971) · Zbl 0225.62108
[2] Brown, L.: On the admissability of invariant estimators of one or more location parameters. Ann. math. Statist. 37, 1087-1136 (1966) · Zbl 0156.39401
[3] Efron, B.; Morris, C.: Limiting the risk of Bayes and empirical Bayes estimators--part I: The Bayes case. J. amer. Statist. assoc. 66, 807-815 (1971) · Zbl 0229.62003
[4] Efron, B.; Morris, C.: Limiting the risk of Bayes and empirical Bayes estimators--part II: The empirical Bayes case. J. amer. Statist. assoc. 67, 130-139 (1972) · Zbl 0231.62013
[5] Efron, B.; Morris, C.: Empirical Bayes on vector observations--an extension of Stein’s method. Biometrika 59, 335-347 (1972) · Zbl 0238.62072
[6] Efron, B.; Morris, C.: Stein’s estimation rule and its competitors--an empirical Bayes approach. J. amer. Statist. assoc. 68, 117-130 (1973) · Zbl 0275.62005
[7] Efron, B.; Morris, C.: Combining possibly related estimation problems. J. royal statist. Soc., B 35, 379-421 (1973) · Zbl 0281.62030
[8] B. Efron and C. Morris, Data analysis using Stein’s estimator and its generalizations, RAND report R-1394-OED. · Zbl 0319.62018
[9] James, W.; Stein, C.: Estimation with quadratic loss. Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, 361-379 (1961) · Zbl 1281.62026
[10] Sclove, S.; Morris, C.; Radhakrishnan, R.: Non-optimality of preliminary test estimators for the mean of a multivariate normal distribution. Ann. math. Statist. 43, 1481-1490 (1972) · Zbl 0249.62029
[11] Stein, C.: Inadmissability of the usual estimator for the mean of a multivariate normal distribution. Proceedings of the third Berkeley symposium on mathematical statistics and probability, 197-206 (1955)