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Abraham Wald

A young Wald
Born October 31, 1902(1902-10-31)
Cluj-Napoca, Austria–Hungary
Died December 13, 1950 (aged 48)
Travancore, India
Nationality Hungarian
Ethnicity Jewish
Fields Mathematics
Institutions Columbia University
Cowles Commission for Research in Economics
Alma mater University of Vienna
Doctoral advisor Karl Menger
Doctoral students Meyer Girshick
Charles Stein
Milton Sobel
Known for Wald's equation
Wald test
Wald's decision theory
Sequential analysis
Sequential probability ratio test
Influences Oskar Morgenstern
John von Neumann
Harold Hotelling
Milton Friedman
Jerzy Neyman
Influenced Aryeh Dvoretzky
Jacob Wolfowitz

Abraham Wald (October 31, 1902(1902-10-31) - December 13, 1950) was a mathematician born in Cluj, in the then Austria–Hungary (present-day Romania) who contributed to decision theory, geometry, and econometrics, and founded the field of statistical sequential analysis.[1]


Life and career

Being a religious Jew, he could not attend school on Saturdays, as was required at the time by the Hungarian school system, and was thus home-schooled by his parents until college.[1] His parents were quite knowledgeable and competent as teachers.[2]

In 1927, he entered graduate school at the University of Vienna, from which he graduated in 1931 with a Ph.D. in mathematics. His advisor there was Karl Menger.[1]

Despite Wald's brilliance, he could not obtain a university position, because of Austrian discrimination against Jews. However, Oskar Morgenstern created a position for Wald in economics. When the Nazis invaded Austria in 1938, the discrimination against Jews intensified. In particular, Wald and his family were persecuted as Jews. Wald was able to emigrate to the United States, at the invitation of the Cowles Commission for Research in Economics, to work on econometrics research.[1]

Wald and his wife died in an airplane crash in the Nilgiri mountains, in southern India, while on an extensive lecture tour at the invitation of the Indian government.[1]

Following his death, Wald was attacked by Sir Ronald A. Fisher FRS; Fisher attacked Wald for being a mathematician without scientific experience who had written an incompetent book on statistics, particularly with regard to the design of experiments.[3] Wald's work was defended by Jerzy Neyman in the following year. Neyman explained Wald's work, particularly with respect to the design of experiments, and diagnosed a fallacy of "fiducial inference", which was a theory proposed by Fisher.[4]

Notable publications

For a complete list, see "The Publications of Abraham Wald". Annals of Mathematical Statistics 23 (1): 29–33. 1952. doi:10.1214/aoms/1177729483. 

  • Wald, Abraham (1939). "A New Formula for the Index of Cost of Living". Econometrica 7 (4): 319–331. doi:10.2307/1906982. 
  • Wald, Abraham (1939). "Contributions to the Theory of Statistical Estimation and Testing Hypotheses". Annals of Mathematical Statistics 10 (4): 299–326. doi:10.1214/aoms/1177732144. 
  • Wald, Abraham (1940). "The Fitting of Straight Lines if Both Variables Are Subject to Error". Annals of Mathematical Statistics 11 (3): 284–300. doi:10.1214/aoms/1177731868. 
  • Wald, Abraham (June 1945). "Sequential Tests of Statistical Hypotheses". The Annals of Mathematical Statistics 16 (2): 117–186. doi:10.1214/aoms/1177731118. 
  • Wald, Abraham (1947). Sequential Analysis. New York: John Wiley and Sons. ISBN 0471918067. "See Dover reprint: ISBN 0486439127" 
  • Wald, Abraham (1950). Statistical Decision Functions. John Wiley and Sons, New York; Chapman and Hall, London. p. ix+179. 

See also


  1. ^ a b c d e Morgenstern, Oskar (1951). "Abraham Wald, 1902-1950". Econometrica 19 (4): 361–367. doi:10.2307/1907462. 
  2. ^ O'Connor, John J.; Robertson, Edmund F., "Abraham Wald", MacTutor History of Mathematics archive, University of St Andrews, .
  3. ^ Fisher 1955.
  4. ^ Neyman 1956.

Further reading



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