JulianaThurston: enhanced formatting for consistency and added references after review

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enhanced formatting for consistency and added references after review

132.62.172.114: researching years→research career

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researching years→research career

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{{Infobox scientist
|name = Abraham Wald
|image = Abraham Wald in his youth.jpg
|image_size =
|caption = A young Wald
|birth_date = {{birth date|1902|10|31}}
|birth_place = [[Cluj-Napoca|Kolozsvár]], [[Kingdom of Hungary]]
|death_date = {{death date and age|1950|12|13|1902|10|31}}
|death_place = [[Nilgiri Mountains]], [[India]]
|residence =
|citizenship =
|nationality = [[Hungary|Hungarian]]
|field = [[Mathematics]] [[Statistics]] [[Mathematical economics|Economics]]
|work_institutions = [[Columbia University]] [[Cowles Commission for Research in Economics]]
|alma_mater = [[Babeș-Bolyai University|King Ferdinand I University]] [[University of Vienna]]
|doctoral_advisor = [[Karl Menger]]
|doctoral_students = [[Herman Chernoff]] [[Milton Sobel]] [[Charles Stein (statistician)|Charles Stein]] 
|known_for = [[Wald's equation]] [[Wald test]] [[Wald distribution]] [[Wald–Wolfowitz runs test]] [[Wald's martingale]] [[Wald's maximin model]] [[Mann–Wald theorem]] [[Decision theory]] [[Sequential analysis]] [[Sequential probability ratio test]]
|author_abbrev_bot =
|author_abbrev_zoo =
|influences = [[Oskar Morgenstern]] [[John von Neumann]] [[Harold Hotelling]] [[Milton Friedman]] [[Jerzy Neyman]]
|influenced = [[Aryeh Dvoretzky]] [[Jacob Wolfowitz]] 
[[John Denis Sargan]], [[Alok Bhargava]]
|prizes =
|footnotes =
|children = [[Robert Wald]]
|signature =
}}

'''Abraham Wald''' ({{IPAc-en|w|ɔː|l|d}}; {{lang-hu|Wald Ábrahám}}, {{lang-yi|אברהם וואַלד}}; {{birth date|1902|10|31|df=y}} – {{death date|1950|12|13|df=y}}) was a [[Hungarian/Hungarian Jewish]] [[mathematician]] who contributed to [[decision theory]], [[geometry]], and [[econometrics]], and founded the field of [[statistical]] [[sequential analysis]].<ref name=Morgenstern1951>{{cite journal
| doi = 10.2307/1907462
| author = Morgenstern, Oskar
| author-link = Oskar Morgenstern
| journal = Econometrica
| volume = 19
| issue = 4
| pages = 361–367
| year = 1951
| title = Abraham Wald, 1902–1950
| publisher = Econometrica, Vol. 19, No. 4
| jstor = 1907462
}}</ref> One of the well known statistical works of his during [[World War II|World War 2]] was how to minimize the damage to bomber aircraft taking into account the [[survivorship bias]] in his calculations.<ref>https://www.researchgate.net/publication/254286514_Abraham_Wald's_Work_on_Aircraft_Survivability</ref> He spent his research career at [[Columbia University]].

== Life and career ==
[[File:Abraham Wald.jpg|thumb|left|upright|Photograph of Abraham Wald from the Mathematisches Forschungsinstitut Oberwolfach.]]
Wald was born on 31 October 1902 in [[Cluj-Napoca|Kolozsvár]], [[Transylvania]], in the [[Kingdom of Hungary]]. A religious [[Jew]], he did not attend school on Saturdays, as was required at the time by the Hungarian school system, and was thus [[home-school]]ed by his parents until college.<ref name=Morgenstern1951/> His parents were quite knowledgeable and competent as teachers.<ref>{{MacTutor Biography|id=Wald}}</ref>

In 1928, he graduated in mathematics from the [[Babeș-Bolyai University|King Ferdinand I University]].<ref>Anuarul Universității Regele Ferdinand I pe anul școlar 1927/28. p. 187. [http://documente.bcucluj.ro/web/bibdigit/periodice/anuaruluniversitatiidincluj/1927-1928/BCUCLUJ_FP_452283_1_1927_1928_007_0001.pdf Online access], University Library in Cluj, Romania.</ref>
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]].<ref name=Morgenstern1951/>

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 Nazi Germany [[Anschluss|annexed 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.<ref name=Morgenstern1951/>

During World War II, Wald was a member of the [[The Statistical Research Group of World War II|Statistical Research Group]] (SRG) at [[Columbia University]], where he applied his statistical skills to various wartime problems.<ref>Wallis, W. Allen. "The Statistical Research Group, 1942-1945." Journal of the American Statistical Association 75, no. 370 (1980): 320-30. doi:10.2307/2287451.</ref> These included methods of sequential analysis and sampling inspection.<ref>{{cite journal|doi=10.1080/01621459.1980.10477469 | volume=75 | issue=370 | title=The Statistical Research Group, 1942–1945 | journal=Journal of the American Statistical Association | pages=320–330| year=1980 | last1=Wallis | first1=W. Allen }}</ref> One of the problems that the SRG worked on was to examine the distribution of [[Survivorship bias#In the military|damage to aircraft returning after flying missions]] so as to provide advice on how to minimize bomber losses to enemy fire. Wald derived a useful means of estimating the damage distribution for all aircraft that flew from the data on the damage distribution of all aircraft that returned.<ref name=Mangel1984>{{cite journal
|title=Abraham Wald's work on aircraft survivability
|last1=Mangel
|first1=Marc
|last2=Samaniego
|first2=Francisco
|journal=Journal of the American Statistical Association
|date=June 1984
|volume=79
|issue=386
|pages=259–267
|jstor=2288257
|doi=10.2307/2288257
}} [http://people.ucsc.edu/~msmangel/Wald.pdf Reprint on author's web site]</ref><ref name=Wald1943>Wald, Abraham. (1943). ''A Method of Estimating Plane Vulnerability Based on Damage of Survivors''. Statistical Research Group, Columbia University. ''[http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA091073 CRC 432 — reprint from July 1980] {{Webarchive|url=https://web.archive.org/web/20151210211957/http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA091073 |date=2015-12-10 }}''. Center for Naval Analyses.</ref> <ref>{{cite book |last1=Wald |first1=Abraham |title='A Method of Estimating Plane Vulnerability Based on Damage of Survivors |date=1980-07-01 |publisher=discover.dtic.mil |edition=ADA091073 |url=https://apps.dtic.mil/sti/citations/ADA091073}}</ref> His work is considered seminal in the then-fledgling discipline of [[operational research]].

Wald and his wife died in 1950 when the Air India plane (VT-CFK, a DC-3 aircraft<ref>[https://aviation-safety.net/database/record.php?id=19501213-1 Incident]</ref>) in which they were travelling crashed near the [[Rangaswamy_Peak_and_Pillar|Rangaswamy Pillar]] in northern part of the [[Nilgiri Mountains]], in southern India, while on an extensive lecture tour at the invitation of the Indian government.<ref name=Morgenstern1951/> He had visited the [[Indian Statistical Institute]] at Calcutta and was to attend the Indian Science Congress at Bangalore in January. Their two children were back at home in the United States.<ref>{{cite news|url=http://spectatorarchive.library.columbia.edu/cgi-bin/columbia?a=d&d=cs19501215-01|title=Prof. Wald Reported Among Victims of India Plane Crash|date=15 December 1950|newspaper=Columbia Daily Spectator|access-date=2018-02-08|issue=52|volume=XCV|page=1}}</ref>

Following his death, Wald was criticized by Sir [[Ronald A. Fisher]] [[Fellow of the Royal Society|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]].<ref name=Fisher1955>{{cite journal
|title=Statistical methods and scientific induction
|author-link=Ronald A. Fisher |first=Ronald |last=Fisher
|journal=Journal of the Royal Statistical Society, Series B
|volume=17
|year=1955
|pages=69–78
|jstor=2983785
|issue=1
}} (criticism of statistical theories of [[Jerzy Neyman]] and Abraham Wald)</ref> 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.<ref name=Neyman1956>{{cite journal
|title=Note on an Article by Sir Ronald Fisher
|author-link=Jerzy Neyman |first=Jerzy |last=Neyman
|journal=Journal of the Royal Statistical Society, Series B
|volume=18
|year=1956
|pages=288–294
|jstor=2983716
|issue=2
}} (reply to Fisher 1955)</ref>
[[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".<ref name=LeCam1986>{{cite book
|title=Asymptotic Methods in Statistical Decision Theory
|author-link=Lucien Le Cam |first=Lucien |last=Le Cam
|year=1986
|pages=xiii
}} (Le Cam 1986)</ref>

Abraham Wald was the father of noted American physicist [[Robert Wald]].

== Notable publications ==
For a complete list, see {{citation
| year = 1952
| title = The Publications of Abraham Wald
| journal = Annals of Mathematical Statistics
| volume = 23
| issue = 1
| pages = 29–33
| doi = 10.1214/aoms/1177729483
| doi-access = free
}}
* {{citation
| doi = 10.2307/1906982
| first = Abraham
| last = Wald
| author-mask = 1
| ref = none
| journal = Econometrica
| volume = 7
| issue = 4
| pages = 319–331
| year = 1939
| title = A New Formula for the Index of Cost of Living
| publisher = Econometrica, Vol. 7, No. 4
| jstor = 1906982
}}
* {{citation
| doi=10.1214/aoms/1177732144
| first=Abraham
| last=Wald
| author-mask = 1
| ref = none|journal=Annals of Mathematical Statistics
| volume=10
| issue=4
| pages=299–326
| year=1939
| title=Contributions to the Theory of Statistical Estimation and Testing Hypotheses
| url=https://projecteuclid.org/download/pdf_1/euclid.aoms/1177732144
| doi-access=free}}
* {{citation
| doi = 10.1214/aoms/1177731868
| first = Abraham
| last = Wald
| author-mask = 1
| ref = none
| journal = Annals of Mathematical Statistics
| volume = 11
| issue = 3
| pages = 284–300
| year = 1940
| title = The Fitting of Straight Lines if Both Variables Are Subject to Error
| doi-access = free
}}
* {{citation
| first = Abraham
| last = Wald
| author-mask = 1
| ref = none
| title = Sequential Tests of Statistical Hypotheses
| journal = The Annals of Mathematical Statistics
| volume = 16
| issue = 2
| date=June 1945
| pages = 117–186
| doi = 10.1214/aoms/1177731118
| doi-access = free
}}
* {{Cite book
| first = Abraham
| last = Wald
| author-mask = 1
| ref = none
| title = Sequential Analysis
| year = 1947
| publisher = [[John Wiley and Sons]]
| location = [[New York City|New York]]
| isbn = 0-471-91806-7
| quote = See Dover reprint: {{isbn|0-486-43912-7}}
}}
* {{cite book
| first=Abraham
| last=Wald
| author-mask = 1
| ref = none
| title=Statistical Decision Functions
| year=1950
| publisher=[[John Wiley and Sons]], New York; [[Chapman and Hall]], London
| page=ix+179
}}<ref>{{citation|author=Robbins, Herbert|author-link=Herbert Robbins|title=Review: A. Wald, ''Statistical decision functions''|journal=Bull. Amer. Math. Soc.|year=1951|volume=57|issue=5|pages=383–384|url=http://projecteuclid.org/euclid.bams/1183516235|doi=10.1090/S0002-9904-1951-09520-8|doi-access=free}}</ref>

== References ==
{{Reflist}}

== Further reading ==
* {{cite journal
| author = Wolfowitz, Jacob
| author-link = Jacob Wolfowitz
| year = 1952
| title = Abraham Wald, 1902–1950
| journal = Annals of Mathematical Statistics
| volume = 23
| issue = 1
| pages = 1–13
| doi = 10.1214/aoms/1177729480
| doi-access = free
}}
* {{Cite web|title=AMS :: Feature Column :: The Legend of Abraham Wald|url=http://www.ams.org/publicoutreach/feature-column/fc-2016-06|website=American Mathematical Society|language=en|access-date=2020-05-29}}

== External links ==
* {{MathGenealogy|id=36887}}

{{Authority control}}

{{DEFAULTSORT:Wald, Abraham}}
[[Category:1902 births]]
[[Category:1950 deaths]]
[[Category:Scientists from Cluj-Napoca]]
[[Category:Austro-Hungarian Jews]]
[[Category:Jewish emigrants from Austria to the United States after the Anschluss]]
[[Category:Presidents of the Institute of Mathematical Statistics]]
[[Category:Fellows of the American Statistical Association]]
[[Category:American statisticians]]
[[Category:Hungarian statisticians]]
[[Category:Econometricians]]

[[Category:20th-century American mathematicians]]
[[Category:Columbia University faculty]]
[[Category:Jewish American scientists]]
[[Category:Victims of aviation accidents or incidents in India]]
[[Category:Hungarian mathematicians]]
[[Category:Babeș-Bolyai University alumni]]
[[Category:University of Vienna alumni]]
[[Category:Mathematical economists]]
[[Category:Hungarian operations researchers]]
[[Category:Functional analysts]]
[[Category:American operations researchers]]
[[Category:20th-century economists]]
[[Category:Fellows of the Econometric Society]]
[[Category:Austro-Hungarian mathematicians]]

Abraham Wald - Revision history

JulianaThurston: enhanced formatting for consistency and added references after review

132.62.172.114: researching years→research career