The Neyman-Pearson Theory after Fifty Years

  • E. L. Lehmann
Open Access
Part of the Selected Works in Probability and Statistics book series (SWPS)


To commemorate the 50th anniversary of the Neyman-Pearson paradigm, this paper sketches some aspects of its development during the past half-century. In particular, the relevance of this approach to data analysis and Bayesian statistics is discussed.


Decision Theory Bayesian Statistic Performance Robustness Asymptotic Optimality Statistical Decision Theory 
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. Andrews, D. F. (1978). Article on "Data Analysis, Exploratory." In Internat. Encycl. of Statist. Kruskal and Tanur, eds. Free Press, New York.Google Scholar
  2. Beran, R. (1974). Asymptotically efficient adaptive rank estimates in location models. Ann. Statist. 2, 63–74.MathSciNetMATHCrossRefGoogle Scholar
  3. Berger, J. (1980). Statistical Decision Theory. Springer, New York.MATHGoogle Scholar
  4. Bickel, P. J. (1981). Minimax estimation of the mean of a normal distribution when the parameter space is restricted. Ann. Statist. 9, 1301–1309.MathSciNetMATHCrossRefGoogle Scholar
  5. Bickel, P. J. (1982). On adaptive estimation. Ann. Statist. 1(9, 647–671.MathSciNetCrossRefGoogle Scholar
  6. Bickel, P. J. (1984). Parametric robustness. Ann. Statist. 12.Google Scholar
  7. Bickel, P. J., and Lehmann, E. L. (1975/1976). Descriptive statistics for nonparametric models. Ann. Statist. 3, 1038–1069; 4, 1139–1158.MathSciNetCrossRefGoogle Scholar
  8. Box, G. E. P. (1980). Sampling and Bayes1 inference in scientific modelling and robustness. J. Roy. Statist. Sec. (A) 243, 383–430.MathSciNetCrossRefGoogle Scholar
  9. Box, G. E. P. (1983). An apology for ecumenism in statistics. In Scientific InferenceData Analysis, and Robustness. Box, Leonard, and Wu, eds. John Wiley, New York.Google Scholar
  10. Box, G. E. P., and Tiao, G. C. (1964). A note on criterion robustness and inference robustness. Biometrika 51, 169–173.MathSciNetMATHGoogle Scholar
  11. Box, G. E. P., and Tiao, G. C. (1973). Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading.MATHGoogle Scholar
  12. Chernoff, H., and Savage, I. R. (1958). Asymptotic normality and efficiency of some nonparametric competitors of the t-test. Ann. Math. Statist. 29, 972–994.MathSciNetCrossRefGoogle Scholar
  13. de Finetti, B. (1937). La prévision: ses lois logiques, ses sources sujectives. Ann. de lInst. Henri Poincaré ?, 1–68.Google Scholar
  14. Kyburg, H., and Smokier, H. (1964), Studies in Subjective Probability, John Wiley, New York.MATHGoogle Scholar
  15. Dempster, A. P. (1983). Purposes and limitations of data Analysis. In Scientific Inference, Data Analysis, and Robustness. Box, Leonard, and Wu, eds. John Wiley, New York.Google Scholar
  16. Diaconis, P., and Freedman, D. (1983). Frequency properties of Bayes rules. In Scientific Inference, Data Analysis, and Robustness. Box, Leonard, and Wu, eds. John Wiley, New York.Google Scholar
  17. Efron, B., and Morris, C. (1973). Stein’s estimation rule and its competitors—an empirical Bayes approach. J. Amer. Statist. Assoc. 68, 117–130.MathSciNetMATHCrossRefGoogle Scholar
  18. Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Phil. Trans. Roy. Soc. (A) 222, 309–368.CrossRefGoogle Scholar
  19. Fisher, R. A. (1935). The Design of Experiments. Oliver and Boyd, Edinburgh.Google Scholar
  20. Freedman, D., and Diaconis, P. (1981). On the histogram as a density estimator: L2 theory. Zeitsch. Wahrsch. 57, 453–476.MathSciNetMATHGoogle Scholar
  21. Freedman, D., and Diaconis, P. (1983). On inconsistent Bayes estimates in the discrete case. Ann. Statist. 11, 1109–1118.MathSciNetMATHGoogle Scholar
  22. Hoaglin, D. C., Mosteller, F., and Tukey, J. W. (1983). Understanding Robust and Exploratory Data Analysis. John Wiley, New York.MATHGoogle Scholar
  23. Hodges, J. L., Jr., and Lehmann, E. L. (1953). The use of previous experience in reaching statistical decisions. Ann. Math. Statist. 23, 396–407.MathSciNetCrossRefGoogle Scholar
  24. Hoeffding, W. (1952). The large-sample power of tests based on permutations of observations. Ann. Math. Statist. 23, 169–192.MathSciNetCrossRefGoogle Scholar
  25. Huber, P. J. (1981). Robust Statistics. John Wiley, New York.MATHCrossRefGoogle Scholar
  26. Jeffreys, H. (1939). The Theory of Probability. Oxford University Press, Oxford.Google Scholar
  27. Jelihovschi, E. (1984). Estimation of Poisson parameters, subject to constraint. Ph.D. dissertation, University of California, Berkeley.Google Scholar
  28. Lehmann, E. L. (1983). Theory of Point Estimation. John Wiley, New York.MATHGoogle Scholar
  29. Lindley, D. (1965). Probability and Statistics. Vol. 2: Inference. Cambridge University Press, Cambridge.MATHGoogle Scholar
  30. Mallows, C. L. (1983). Data description. In Scientific Inference, Data Analysis, and Robustness. Box, Leonard, and Wu, eds. John Wiley, New York.Google Scholar
  31. Mosteller, F., and Tukey, J. W. (1977). Data Analysis and Regression. John Wiley, New York.Google Scholar
  32. Mosteller, F., and Wallace, D. (1964). Inference and Disputed Authorship: The Federalist. Addison-Wesley, Reading.MATHGoogle Scholar
  33. Neyman, J. (1937). Outline of a theory of statistical estimation based on the classical theory of probability. Phil. Trans. Roy. Soc. (A) 236, 333–380.CrossRefGoogle Scholar
  34. Neyman, J., and Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Phil. Trans. Roy. Soc. (A) 231, 289–337.CrossRefGoogle Scholar
  35. Pearson, E. S. (1966). The Neyman-Pearson story: 1926–1934. In Research Papers in Statistics: Festschrift for J. Neyman. F. N. David, ed. John Wiley, New York.Google Scholar
  36. Raiffa, H., and Schlaifer, R. (1961). Applied Statistical Decision Theory. Harvard University Pres, Cambridge.Google Scholar
  37. Reid, C. (1982). Neyman-From Life. Springer, New York.MATHCrossRefGoogle Scholar
  38. Savage, L. J. (1954). Foundations of Statistics. John Wiley, New York. 2nd revised ed., Dover (1972).MATHGoogle Scholar
  39. Scott, D. W. (1979). On optimal and data-based histograms. Biomet- rika 66, 605–610.MATHCrossRefGoogle Scholar
  40. Stein, C. (1956). Efficient nonparametric testing and estimation. Proc. Third Berkeley Symp. Math. Statist. and Prob. 1, 187–196.Google Scholar
  41. Stone, C. J. (1975). Adaptive maximum likelihood estimators of a location parameter. Ann. Statist. 3, 267–284.MathSciNetMATHCrossRefGoogle Scholar
  42. Stone, C. J. (1981). Admissible selection of an accurate and parsimonious normal linear regression model. Ann. Statist. 9, 475–485.MathSciNetMATHCrossRefGoogle Scholar
  43. Student [W. S. Gosset] (1908). On the probable error of a mean. Biometrika 6, 1–25.Google Scholar
  44. Tan, W. Y. (1982). Sampling distributions and robustness of t, F and variance-ratio in two samples and ANOVA models with respect to departure from normality. Communications in Statistics, Theory and Methods 11 (No. 22), 2485–2511.MATHGoogle Scholar
  45. Thisbed, R. (1982). Decision theoretic regression diagnostics. In Statistical Decision Theory and Related Topics. Gupta and Berger, eds. Academic Press, New York. Vol. II, pp. 363–382.Google Scholar
  46. Tukey, J. W., and McLaughlin, D. H. (1963). Less vulnerable confidence and significance procedures for location based on a single sample: Trimraing/Winsorization 1. Sankhya 25, 331–352.MathSciNetMATHGoogle Scholar
  47. Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley, Reading.MATHGoogle Scholar
  48. Wald, A. (1950). Statistical Decision Functions. John Wiley, New York.MATHGoogle Scholar

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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • E. L. Lehmann
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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