Institute of Mathematical Statistics Lecture Notes - Monograph Series

Some History of Optimality

Erich L. Lehmann

Full-text: Open access


This paper gives an account of the history of both small- and large-sample optimality for both estimation and testing. It covers this history from the beginnings by Laplace and Gauss to the ongoing research on optimal multiple comparison procedures, and also includes the optimality of designs.

Chapter information

Javier Rojo, ed., Optimality: The Third Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 11-17

First available in Project Euclid: 3 August 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

optimality estimation testing design maximum likelihood Neyman-Pearson lemma

Copyright © 2009, Institute of Mathematical Statistics


Rojo, Javier. Some History of Optimality. Optimality, 11--17, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-LNMS5703.

Export citation


  • [1] Barndorff-Nielsen, O. E. and Cox, D. R. (1994). Inference and Asymptotics. Chapman & Hall, London.
  • [2] Box, G. E. P. and Wilson, K. B. (1951). On the experimental attainment of optimum conditions. J. Roy. Statist. Soc. Ser. B 13 1–45.
  • [3] Chatterjee, S. K. (2003). Statistical Thought. Oxford Univ. Press.
  • [4] Efron, B. (1982). Maximum likelihood and decision theory. Ann. Statist. 10 309–368.
  • [5] Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Phil. Trans. Roy. Soc. London Ser. A 222 401–415.
  • [6] Fisher, R. A. (1925). Theory of statistical estimation. Cambridge Philos. Soc. 22 700–725.
  • [7] Hald, A. (1998). A History of Mathematical Statistics - from 1750 to 1930. Wiley, New York.
  • [8] Huber, P. (1964). Robust estimation of a location parameter. Ann. Math. Statist. 35 73–101.
  • [9] Huber, P. (1965). A robust version of the probability ratio test. Ann. Math. Statist. 36 1753–1758.
  • [10] Huber, P. (1975). Applications vs. abstraction: The selling out of mathematical statistics? In Proc. Conference on Directions of Mathematical Statistics. Suppl. Adv. Prob. 7 84–89.
  • [11] Kiefer, J. C. (1959). Optimum experimental designs (with discussion). J. Roy. Statist. Soc. Ser. B 21 273–319. (Reprinted in Kotz and Johnson (1992). Breakthroughs in Statistics, Vol. 1. Springer.)
  • [12] Kimball, G. E. (1958). A critique of operations research. J. Wash. Acad. Sci. 48 33–37.
  • [13] Kotz, S. and Johnson, N. L. (Eds. 1992, 1997). Breakthroughs in Statistics 1. Springer, New York.
  • [14] Le Cam, L. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes’ estimates. Univ. of Calif. Publ. in Statist. 1 277–330.
  • [15] Le Cam, L. (1990). Maximum likelihood - an introduction. ISI Review 58 153–171.
  • [16] Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses, 3rd ed. Springer, New York.
  • [17] Neyman, J. and Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Phil. Trans. Roy. Soc. Ser. A 231 289–337.
  • [18] Neyman, J. and Pearson, E. S. (1936, 1938). Contributions to the theory of testing statistical hypotheses. Statist. Res. Memoirs 1 1–37; 2 25–57.
  • [19] Pearson, E. S. (1939). “Student” as a statistician. Biometrika 30 210–250.
  • [20] Shaffer, J. P. (2004). Optimality results in multiple hypothesis testing. In Proceedings of the First Lehmann Symposium (J. Rojo and V. Pérez-Abreu, eds.). IMS Lecture Notes Monogr. Ser. 44 11–35. Inst. Math. Statist., Beachwood, OH.
  • [21] Shaffer, J. P. (2006). Recent developments towards optimality in multiple hypothesis testing. In Proceedings of the Second Lehmann Symposium (J. Rojo, ed.). IMS Lecture Notes Monogr. Ser. 49 16–32. Inst. Math. Statist., Beachwood, OH.
  • [22] Shao, J. (1999). Mathematical Statistics. Springer, New York.
  • [23] Stigler, S. (1986). The History of Statistics. Harvard Univ. Press, Cambridge, MA.
  • [24] Tukey, J. W. (1961). Statistical and quantitative methodology. In Trends in Social Science (D. P. Ray, ed.). Philosophical Library, New York. (Reprinted in Vol. III of Tukey’s Collected Works.)
  • [25] Tukey, J. W. (1962). The future of data analysis. Ann. Math. Statist. (Reprinted in Vol. III of Tukey’s Collected Works.)
  • [26] Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Amer. Math. Soc. 54 426–482.
  • [27] Wald, A. (1950). Statistical Decision Functions. Wiley, New York.
  • [28] Wald, A. and Wolfowitz, J. (1948). Optimum character of the sequential probability ratio test. Ann. Math. Statist. 19 326–339.