A young Wald
October 31, 1902|
|Died||December 13, 1950
Cowles Commission for Research in Economics
|Alma mater||University of Vienna|
|Doctoral advisor||Karl Menger|
|Doctoral students||Meyer Girshick
|Known for||Wald's equation
Sequential probability ratio test
John von Neumann
Abraham Wald (Hungarian: Wald Ábrahám, October 31, 1902 – 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 Jewish person, 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 1928 he graduated in mathematics from the King Ferdinand I University in Romanian language. 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 immigrate to the United States, at the invitation of the Cowles Commission for Research in Economics, to work on econometrics research.
During World War II, Wald applied his statistical skills when considering how to minimize bomber losses to enemy fire. Researchers from the Center for Naval Analyses had conducted a study of the damage done to aircraft that had returned from missions, and had recommended that armor be added to the areas that showed the most damage. Wald noted that the study only considered the aircraft that had survived their missions—the bombers that had been shot down were not present for the damage assessment. The holes in the returning aircraft, then, represented areas where a bomber could take damage and still return home safely. Wald proposed that the Navy instead reinforce the areas where the returning aircraft were unscathed, since those were the areas that, if hit, would cause the plane to be lost. This is still considered today seminal work in the then-fledgling discipline of operational research.
Following his death, Wald was criticized 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 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. Lucien Le Cam credits him in his own book, Asymptotic Methods in Statistical Decision Theory: "The ideas and techniques used reflect first and foremost the influence of Abraham Wald's writings".
Abraham Wald was the father of noted American physicist Robert Wald.
- Wald, Abraham (1939). "A New Formula for the Index of Cost of Living". Econometrica (Econometrica, Vol. 7, No. 4) 7 (4): 319–331. doi:10.2307/1906982. JSTOR 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 0-471-91806-7.
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.
- Morgenstern, Oskar (1951). "Abraham Wald, 1902–1950". Econometrica (Econometrica, Vol. 19, No. 4) 19 (4): 361–367. doi:10.2307/1907462. JSTOR 1907462.
- O'Connor, John J.; Robertson, Edmund F., "Abraham Wald", MacTutor History of Mathematics archive, University of St Andrews.
- Anuarul Universității Regele Ferdinand I pe anul școlar 1927/28. p. 187. Online access, University Library in Cluj, Romania.
- Mangel, Marc; Samaniego, Francisco (June 1984). "Abraham Wald's work on aircraft survivability". Journal of the American Statistical Association 79 (386): 259–267. doi:10.2307/2288257. JSTOR 2288257. Reprint on author's web site
- Wald, Abraham. (1943). A Method of Estimating Plane Vulnerability Based on Damage of Survivors. Statistical Research Group, Columbia University. CRC 432 — reprint from July 1980. Center for Naval Analyses.[dead link]
- Fisher, Ronald (1955). "Statistical methods and scientific induction". Journal of the Royal Statistical Society, Series B 17 (1): 69–78. JSTOR 2983785. (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 18 (2): 288–294. JSTOR 2983716. (reply to Fisher 1955)
- Le Cam, Lucien (1986). Asymptotic Methods in Statistical Decision Theory. pp. xiii. (Le Cam 1986)
- Robbins, Herbert (1951). "Review: A. Wald, Statistical decision functions". Bull. Amer. Math. Soc. 57 (5): 383–384. doi:10.1090/S0002-9904-1951-09520-8.
- Wolfowitz, Jacob (1952). "Abraham Wald, 1902–1950". Annals of Mathematical Statistics 23 (1): 1–13. doi:10.1214/aoms/1177729480.