Abraham Wald

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 Statistics Economics
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]

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 while on an extensive lecture tour at the invitation of the Indian government.^[1]

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

• Sequential probability ratio test (SPRT)
• Wald distribution

References

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, http://www-history.mcs.st-andrews.ac.uk/Biographies/Wald.html .

Further reading

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