Abraham Wald

Abraham Wald
A young Wald
Born	(1902-10-31)October 31, 1902 Cluj-Napoca, Austria–Hungary
Died	Travancore, India
Nationality	Hungarian
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 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 (Hungarian: Wald Ábrahám, (1902-10-31)October 31, 1902 – December 13, 1950(1950-12-13)) 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 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.

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 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.

Notable publications

For a complete list, see

See also

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

External links

• Abraham Wald at the Mathematics Genealogy Project