Herman Wold

Herman Wold
Born	(1908-12-25)25 December 1908 Skien, Norway
Died	16 February 1992(1992-02-16) (aged 83)
Nationality	Swedish
Alma mater	University of Stockholm
Known for	Wold's theorem MA(${\displaystyle \infty }$)representation of stationary stochastic processes Wold decomposition (Operator theory) Cramér–Wold theorem Time series analysis Utility theory Consumer demand Latent variable Structural equation models Consistentleast squaresestimation of recursivetriangular systems Causal inference in observational studies Partial least squares regression
Scientific career
Fields	Statistics Econometrics
Institutions	Uppsala University
Doctoral advisor	Harald Cramér
Doctoral students	Sten Malmquist Peter Whittle Karl Jöreskog

Herman Ole Andreas Wold (25 December 1908 – 16 February 1992) was a Norwegian-born econometrician and statistician who had a long career in Sweden. Wold was known for his work in mathematical economics, in time series analysis, and in econometric statistics.

In mathematical statistics, Wold contributed the Cramér–Wold theorem characterizing the normal distribution and developed the Wold decomposition in time series analysis. In microeconomics, Wold advanced utility theory and the theory of consumer demand. In multivariate statistics, Wold contributed the methods of partial least squares (PLS) and graphical models. Wold's work on causal inference from observational studies was decades ahead of its time, according to Judea Pearl.^[1]

Early life

Herman Wold was born in Skien, Southern Norway. He was the youngest in a family of six brothers and sisters. In 1912 the family moved to Sweden and became Swedish citizens. Herman's father had a small fur and hide business.

과학적 업적

Herman Wold는 60년 동안 길고 생산적인 경력을 가지고 있었다.

Harald Cramér와 함께 공부하기

1927년에 월드는 수학을 공부하기 위해 스톡홀름 대학에 등록했다. Harald Cramér가 보험수리적수학통계학과 교수로 임명되었기 때문에 적절한 시기였다. Wold는 나중에 "Cramér의 첫 번째 학생 그룹에 속한 것은 행운이었고, 이는 단순히 과장될 수 없는 장점이었다"고 썼다.

1930년 졸업 후 Wold는 보험회사에서 일했다; 그는 또한 Cramér와 함께 사망률 데이터를 연구했고 나중에 보험회사들을 위해 관세를 고안했다. 그는 Cramér를 감독자로 하여 확률적인 과정에 관한 박사과정을 연구하기 시작했다. Wold와 Cramér가 몇몇 공동 작업을 했다는 논문과는 별도로, 가장 잘 알려진 결과는 Cramér-Wold 정리(1936년)이다.

시계열 및 월드 분해

월드의 논문 A Study in the stater time series 분석은 중요한 공헌이었다. 주된 결과는 정지 계열이 결정론적 요소들의 합으로 표현되고 그 자체가 무한 이동 평균으로 표현될 수 있는 확률적 요소로서 표현되는 "Wold discolation"이었다. 이를 넘어 영국 통계학자, 주로 우드니 율레(Udny Yule)의 개별적 과정에 대한 연구와 러시아 수학자들이 만든 고정적 확률적 과정 이론(주로 A)이 처음으로 한 자리에 모였다. 네. 킨친. 월드의 일변량 시계열 결과는 그의 제자 피터 위틀에 의해 다변량 시계열로 일반화되었다.

월드 분해와 관련 월드의 정리는 버링의 조화 분석의 인자화 정리와 선형 연산자의 불변 서브스페이스에 대한 관련 작업에 영감을 주었다.

소비자수요이론

1938년 정부 위원회는 월드를 스웨덴의 소비자 수요에 대한 계량학적 연구를 하도록 임명했다. 그 결과는 1940년에 발표되었다. 병행하여 수요이론에 힘썼다. 그의 저서 수요 분석(1952)은 수요 이론, 확률적 과정 이론, 회귀 이론과 스웨덴 자료에 대한 그의 연구를 종합했다.^[2]

Systems of simultaneous equations and causal inference

In 1943 and 1944, Trygve Haavelmo put forward his ideas on the simultaneous equations model, arguing that systems of simultaneous equations should be central in econometric research. Wold noted some limitation of the maximum-likelihood approach favoured by Haavelmo and the Cowles Commission; Wold cautioned that the literature contained some exaggerated claims for the superiority of maximum-likelihood estimation.

In 1945 to 1965, Wold proposed and elaborated on his "recursive causal chain" model, which was more appropriate for many applications, according to Wold: For such "recursive causal chain" models, the least squares method was computationally efficient and enjoyed superior theoretical properties, which it lacked for general time-series models. Wold's writings on causality and recursive-chain models have been recognized^{[citation needed]} as scientific inventions by recent work on causality and graphical models in statistics, especially by Judea Pearl and Nanny Wermuth.

Multivariate analysis and partial least squares

At the end of his career, Wold turned away from econometric modelling and developed multivariate techniques for what he called "soft" modelling. Some of these methods were developed through interactions with his student K. G. Jöreskog, although the latter's focus was primarily on maximum likelihood methods.

Appointments

The story of Wold's academic appointments is briefly told. In 1942 he became professor of statistics at Uppsala University and he stayed there until 1970. He then moved to Gothenburg, retiring from there in 1975.

In 1960 Wold became a member of the Royal Swedish Academy of Sciences. He was a member of the Prize Committee for the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel from 1968 to 1980.

Selected writings by H. O. A. Wold

• 1938. A Study in the Analysis of Stationary Time Series, Almqvist & Wiksell
• 1949. Statistical Estimation of Economic Relationships, in Econometrica,
• 1952. Demand Analysis: A Study in Econometrics, with Lars Juréen.
• 1954. "Causality and Econometrics," Econometrica, 22(2), p p. 162-177.
• 1964.Econometric model building : essays on the causal chain approach (edited by Herman O.A. Wold).
• 1969. "Econometrics as Pioneering in Nonexperimental Model Building," Econometrica, 37(3), p p. 369-381.
• 1980. The Fix-Point Approach to Interdependent Systems (edited by Herman Wold), North-Holland.
• 1982. Systems under Indirect Observation: Causality, Structure, Prediction (edited by K. G. Jöreskog and H. Wold), North-Holland.

There is an extensive bibliography published with the ET interview (below).

See also

Notes

References

Autobiography

• J. Gani, ed. (1982). The Making of Statisticians, New York: Springer-Verlag. This has a chapter in which Wold tells the story of his life.
• See the ET interview under External Links.

Discussion

• Svante Wold "Wold, Herman Ole Andreas";, pp. 213–4 in Leading Personalities in Statistical Sciences from the Seventeenth Century to the Present, (ed. N. L. Johnson and S. Kotz) 1997. New York: Wiley. Originally published in Encyclopedia of Statistical Science.

External links

• ET Interviews: Professor H. O. A. Wold on the Econometric Theory page.
• New School: Herman Wold, 1908-1992
• Herman Wold at the Mathematics Genealogy Project
• Newspaper clippings about Herman Wold in the 20th Century Press Archives of the ZBW

There is a photograph at

• H. O. A. Wold on the Portraits of Statisticians page.

See also (external links, again)

• Cramér–Wold theorem
• Wold decomposition