List of Important Publications in Statistics - Mathematical Statistics

Mathematical Statistics

Mathematical Methods of Statistics

Author: Harald Cramér

Publication data: Princeton Mathematical Series, vol. 9. Princeton University Press, Princeton, N. J., 1946. xvi+575 pp. (A first version was published by Almqvist & Wiksell in Uppsala, Sweden, but had little circulation because of World War II.)

Description: Carefully written and extensive account of measure-theoretic probability for statisticians, along with careful mathematical treatment of classical statistics.

Importance: Made measure-theoretic probability the standard language for advanced statistics in the English-speaking world, following its earlier adoption in France and the USSR.

Statistical Decision Functions

Author: Abraham Wald

Publication data: 1950. John Wiley & Sons.

Description: Exposition of statistical decision theory as a foundations of statistics. Included earlier results of Wald on sequential analysis and the sequential probability ratio test and on Wald's complete class theorem characterizing admissible decision rules as limits of Bayesian procedures.

Importance: Raised the mathematical status of statistical theory and attracted mathematical statisticians like John von Neumann, Aryeh Dvoretzky, Jacob Wolfowitz, Jack C. Kiefer, and David Blackwell, providing greater ties with economic theory and operations research. Spurred further work on decision theory.

Testing Statistical Hypotheses

Author: Erich Leo Lehmann

Publication data: 1959. John Wiley & Sons.

Description: Exposition of statistical hypothesis testing using the statistical decision theory of Abraham Wald, with some use of measure-theoretic probability.

Importance: Made Wald's ideas accessible. Collected and organized many results of statistical theory that were scattered throughout journal articles, civilizing statistics.