| 词条 | Abraham Wald |
| 释义 |
|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, Austria–Hungary (now Cluj-Napoca, Romania) |death_date = {{death date and age|1950|12|13|1902|10|31}} |death_place = Nilgiri Mountains, India |residence = |citizenship = |nationality = Hungarian |field = Mathematics Statistics Economics |work_institutions = Columbia University Cowles Commission for Research in Economics |alma_mater = University of Cluj University of Vienna |doctoral_advisor = Karl Menger |doctoral_students = Herman Chernoff Milton Sobel Charles Stein |known_for = Wald's equation Wald test 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 = |signature = }} Abraham Wald ({{IPAc-en|w|ɔː|l|d}}; {{lang-hu|Wald Ábrahám}}; {{birth date|1902|10|31|df=y}} – {{death date|1950|12|13|df=y}}) was a Hungarian mathematician who contributed to decision theory, geometry, and econometrics, and founded the field of statistical sequential analysis.[1] He spent his researching years at Columbia University. Life and careerWald was born on 31 October 1902 in Cluj, in Transylvania in Austria–Hungary (now in Romania). 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-schooled by his parents until college.[1] His parents were quite knowledgeable and competent as teachers.[2] In 1928, he graduated in mathematics from the King Ferdinand I University.[3] 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] During World War II, Wald was a member of the Statistical Research Group (SRG) where he applied his statistical skills to various wartime problems. These included methods of sequential analysis and sampling inspection.[4] One of the problems that the SRG worked on was to examine the distribution of damage to aircraft to provide advice on how to minimize bomber losses to enemy fire. There was an inclination within the military to consider providing greater protection to parts that received more damage but Wald made the assumption that damage must be more uniformly distributed and that the aircraft that did return or show up in the samples were hit in the less vulnerable parts. 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.[5][6] His work is considered seminal in the then-fledgling discipline of operational research. Wald and his wife died when the Air India plane in which they were travelling crashed in the Nilgiri Mountains, in southern India, while on an extensive lecture tour at the invitation of the Indian government.[1] 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.[7] 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.[8] 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.[9] 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".[10]Abraham Wald was the father of noted American physicist Robert Wald. Notable publicationsFor a complete list, see {{cite journal | 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 = 10.2307/1906982 | first = Abraham | last = Wald | 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 }}
| doi = 10.1214/aoms/1177732144 | first = Abraham | last = Wald | 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 }}
| doi = 10.1214/aoms/1177731868 | first = Abraham | last = Wald | 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 }}
| first = Abraham | last = Wald | 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 }}
| first = Abraham | last = Wald | title = Sequential Analysis | year = 1947 | publisher = John Wiley and Sons | location = New York | isbn = 0-471-91806-7 | quote = See Dover reprint: {{isbn|0-486-43912-7}} }}
|first=Abraham |last=Wald |title=Statistical Decision Functions |year=1950 |publisher=John Wiley and Sons, New York; Chapman and Hall, London |page=ix+179 }}[11] See also
References1. ^1 2 3 4 {{cite journal | doi = 10.2307/1907462 | author = Morgenstern, Oskar | authorlink = 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}} 2. ^{{MacTutor Biography|id=Wald}} 3. ^Anuarul Universității Regele Ferdinand I pe anul școlar 1927/28. p. 187. Online access, University Library in Cluj, Romania. 4. ^{{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 }} 5. ^{{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}} Reprint on author's web site 6. ^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. 7. ^{{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|last=|first=|date=15 December 1950|newspaper=Columbia Daily Spectator|access-date=2018-02-08|archive-url=|archive-date=|dead-url=|issue=52|volume=XCV|page=1}} 8. ^{{cite journal|title=Statistical methods and scientific induction|authorlink=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) 9. ^{{cite journal|title=Note on an Article by Sir Ronald Fisher|authorlink=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) 10. ^{{cite book|title=Asymptotic Methods in Statistical Decision Theory|authorlink=Lucien Le Cam |first=Lucien |last=Le Cam|year=1986|pages=xiii}} (Le Cam 1986) 11. ^{{cite journal|author=Robbins, Herbert|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}} Further reading
| author = Wolfowitz, Jacob | authorlink = 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 }} External links
25 : 1902 births|1950 deaths|People from Cluj-Napoca|Romanian Jews|Austro-Hungarian Jews|American people of Romanian-Jewish descent|Presidents of the Institute of Mathematical Statistics|Fellows of the American Statistical Association|American statisticians|Hungarian statisticians|Econometricians|Mathematical analysts|20th-century American mathematicians|Columbia University faculty|Jewish American scientists|Victims of aviation accidents or incidents in India|Hungarian mathematicians|University of Vienna alumni|Mathematical economists|Hungarian operations researchers|Functional analysts|American operations researchers|20th-century economists|Fellows of the Econometric Society|Austro-Hungarian mathematicians |
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