Abraham Wald

Abraham Wald
A young Wald
Born	(1902-10-31)October 31, 1902 Cluj-Napoca, Austria–Hungary
Died	December 13, 1950(1950-12-13) (aged 48) Travancore, India
Nationality	Hungarian
Alma mater	University of Vienna
Known for	Wald's equation Wald test Wald's decision theory Sequential analysis Sequential probability ratio test
Scientific career
Fields	Mathematics Statistics Economics
Institutions	Columbia University Cowles Commission for Research in Economics
Doctoral advisor	Karl Menger
Doctoral students	Meyer Girshick Charles Stein Milton Sobel

Abraham Wald ((1902-10-31)October 31, 1902 – (1950-12-13)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. He spent his researching years at Columbia University.

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. His parents were quite knowledgeable and competent as teachers.

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.

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.

Wald applied his statistical skills in World War II to the problem of bomber losses to enemy fire. A study was made of the damage to returning aircraft and it was proposed to add armor to those areas that showed most damage. Wald's unique insight was that the important population was those bombers that didn't return and the optimal solution was to add armor to the areas that showed no damage - since none of those planes made it back.

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.

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, Fisher claimed; Fisher particularly criticized Wald's work on the design of experiments, alleging ignorance of the basic ideas of the subject, as set out by Fisher and Frank Yates. 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.

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). Econometrica, Vol. 7, No. 4: 319–331. doi:10.2307/1906982. Retrieved 2008-06-27.
• 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. {{cite journal}}: |access-date= requires |url= (help)
• 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. {{cite journal}}: |access-date= requires |url= (help)
• Wald, Abraham (1945). "Sequential Tests of Statistical Hypotheses". The Annals of Mathematical Statistics. 16 (2): 117–186. doi:10.1214/aoms/1177731118. {{cite journal}}: Unknown parameter |month= ignored (help)
• Wald, Abraham (1947). Sequential Analysis. New York: John Wiley and Sons. ISBN 0471918067. See Dover reprint: ISBN 0-486-43912-7
• Wald, Abraham (1950). Statistical Decision Functions. John Wiley and Sons, New York; Chapman and Hall, London. p. ix+179.

See also

• Sequential probability ratio test (SPRT)
• Wald distribution
• Wald–Wolfowitz runs test

References

• Fisher, Ronald "Statistical methods and scientific induction" J. Roy. Statist. Soc. Ser. B. 17 (1955), 69–78. (criticism of statistical theories of Jerzy Neyman and Abraham Wald)
• Neyman, Jerzy (1956). "Note on an Article by Sir Ronald Fisher". Journal of the Royal Statistical Society. Series B (Methodological). Vol. 18, no. 2. pp. 288–294. JSTOR 2983716 (reply to Fisher 1955)

Further reading

• Wolfowitz, Jacob (1952). "Abraham Wald, 1902–1950". Annals of Mathematical Statistics. 23 (1): 1–13. doi:10.1214/aoms/1177729480.