Erich L. Lehmann’s Work on Decision Theory

  • Javier Rojo
Open Access
Part of the Selected Works in Probability and Statistics book series (SWPS)


This chapter collects some of Erich’s work on areas that attracted his attention during the early years in his professional career. Thus, the papers discuss the concepts of completeness (minimal complete families and complete sufficient statistics), minimal sufficiency, admissibility, invariance, unbiasedness, and minimaxity.


Loss Function Decision Theory Minimax Estimator Favorable Distribution Convex Loss Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    G. W. Brown. On Small-Sample Estimation. Ann. Math. Statist., Vol. 18, No. 4, pp. 582-585, 1947.MATHCrossRefGoogle Scholar
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    R. R. Bahadur and L. A. Goodman. Impartial Decision Rules and Sufficient Statistics. Ann. Math. Statist., Vol. 23, No. 4, pp. 553-562, 1952.MathSciNetMATHCrossRefGoogle Scholar
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    R. R. Bahadur. Sufficiency and Statistical Decision Functions. Ann. Math. Statist., Vol. 25, No. 3, pp. 423-462, 1954.MathSciNetCrossRefGoogle Scholar
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    R. R. Bahadur and E. L. Lehmann. Two comments on sufficiency and statistical decision functions. Ann. Math. Statist., Vol. 26, pp. 139-142, 1955.MathSciNetMATHCrossRefGoogle Scholar
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    R. E. Bechhofer. A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances. Ann. Math. Statist., Vol. 25, No. 1, pp. 16-39, 1954.MathSciNetMATHCrossRefGoogle Scholar
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    R. E. Bechhofer and M. Sobel. A Single-Sample Multiple Decision Procedure for Ranking Variances of Normal Populations. Ann. Math. Statist., Vol. 25, No. 2, pp. 273-289, 1954.MathSciNetMATHCrossRefGoogle Scholar
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    R. E. Bechhofer, S. Elmaghraby, and N. Morse. A Single-Sample Multiple-Decision Procedure for Selecting the Multinomial Event Which Has the Highest Probability. Ann. Math. Statist., Vol. 30, No. 1, pp. 102-119, 1959.MathSciNetMATHCrossRefGoogle Scholar
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    F. N. David and J. Neyman. Extension of the Markoff Theorem on Least Squares. Statistical Research Memoirs,Vol. II, London, pp. 105-116, 1938.Google Scholar
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    P. R. Halmos and L. J. Savage. Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics. Ann. Math. Statist., Vol. 20, No. 2, pp. 225-241, 1949.MathSciNetMATHCrossRefGoogle Scholar
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    J. L. Hodges, Jr. and E. L. Lehmann. Some problems in minimax point estimation. Ann. Math. Statist., Vol. 21, pp. 182-197, 1950.MathSciNetMATHCrossRefGoogle Scholar
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    J. L. Hodges, Jr. and E. L. Lehmann. Some applications of the Cramer-Rao inequality. Proc. Second Berkeley Symp. Math. Statist. Prob., University of California Press13-22, 1951.Google Scholar
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    J. L. Hodges, Jr. and E. L. Lehmann. The use of previous experience in reaching statistical decisions. Ann. Math. Statist., Vol. 23, pp. 396-407, 1952.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    D. Landers and L. Rogge. Minimal Sufficient a-Fields and Minimal Sufficient Statistics. Two Counterexamples. Ann. Math. Statist., Vol. 43, No. 6, pp. 2045-2049, 1972.MathSciNetMATHCrossRefGoogle Scholar
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    E. L. Lehmann. On families of admissible tests. Ann. Math. Statist., Vol. 18, pp. 97-104, 1947.MathSciNetMATHCrossRefGoogle Scholar
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    E. L. Lehmann and H. Scheffe. Completeness, similar regions and unbiased estimation. Part I. Sankhya, Vol. 10, pp. 305-340, 1950.MathSciNetMATHGoogle Scholar
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    E. L. Lehmann. A general concept of unbiasedness. Ann. Math. Statist., Vol. 22, pp. 587-591, 1951.MathSciNetMATHCrossRefGoogle Scholar
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    E. L. Lehmann. On the existence of least favorable distributions. Ann. Math. Statist., Vol. 23, pp. 408-416, 1952.MathSciNetMATHCrossRefGoogle Scholar
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    E. L. Lehmann and C. Stein. The admissibility of certain invariant statistical tests involving a translation parameter. Ann. Math. Statist., Vol. 24, pp. 473-479, 1953.MathSciNetMATHCrossRefGoogle Scholar
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    E. L. Lehmann. On a theorem of Bahadur and Goodman. Ann. Math. Statist., Vol. 37, pp. 1-6, 1966.MathSciNetMATHCrossRefGoogle Scholar
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    E. L. Lehmann and G. Casella. Theory of Point Estimation, 2nd Edition. Springer-Verlag, 1998.Google Scholar
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    E. L. Lehmann.Reminiscences of a Statistician: The Company I Kept Springer, 2008. Google Scholar
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    T. S. Pitcher. Sets of Measures not Admitting Necessity and Sufficient Statistics or Subfields. Ann. Math. Statist., Vol. 28, No. 1, pp. 267-268, 1957.MathSciNetMATHCrossRefGoogle Scholar
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    J. Rojo. On Lehmann’s General Concept of Unbiasedness and the Existence of L-unbiased Estimators. Ph.D. Thesis, Department of Statistics, University of California at Berkeley, 1984.Google Scholar
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    A. Wald. Statistical Decision Functions. John Wiley & Sons, 1950.Google Scholar

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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of StatisticsRice UniversityHoustonUSA

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