Fiancée's death and his 1935 expedition to Greenland
Elfving was engaged to a young woman, who died in 1935, probably from tuberculosis. The grieving parents of his fiancée helped Elfving contact the Danish Geodetic Institute, which hired him as the mathematician for a cartographic expedition
to Western Greenland in the summer of 1935.[6] Elfving was photographed while he made theodolite measurements and peered from a tent.[4] Heavy rains forced the expedition to remain sheltered in their tents for three days, during which Elfving started to think about the best locations to take measurements for least squares estimation.[8]
In statistics, Elfving is known as one of the founders of the modern theory of the optimal design of experiments.[1][2][9] While accompanying a surveying expedition to western Greenland, extended and intense rains left Elving with three days in his tent, during which time he considered the best locations of observations to estimate parameters of linear models.[2][8][9] Elfving's ideas appeared in his paper on the optimal design of experiments for estimating linear models. This paper also introduced concepts from convex geometry, including "Elfving sets"[10] and Elfving's theorem.[11][12] Being symmetric, Elfving sets are formed by the union of a set and its reflection through the origin, −S ∪ S.[13][14][15] According to Chernoff (1999, p. 204), Elfving was generous in crediting others' results: His paper in the Cramér-festschrift acknowledged unpublished notes of L. J. Savage; Elfving was a referee for the fundamental paper on optimal designs by Kiefer and Wolfowitz.[16][17]
Other statistical contributions
As a Professor at the University of Helsinki, Elfving was responsible for writing Finnish language texts, which were used for decades. In his texts and reviews, Elfving emphasized the decision-theoretic foundations of statistics, following Neyman, Pearson, and Wald, and recognized the value of Bayesian methods in statistics and also in operations research.[18] Elfving introduced the statistical symbol for probabilistic independence ⊥⊥, which is a stronger condition than orthogonality ⊥, by the 1950s.[19]
He also supervised many students. Elja Arjas is known for his work on inference on stochastic processes and reliability theory, as well as for his supervision of Esa Nummelin and Hannu Oja.[21]Johann Fellman has studied optimal designs for nonsingular or nondifferentiable information functions as well economic theory, and genetics (particularly the frequency of twin births) and for his supervision of Kenneth Nordström and Katarina Juselius.[22][23]
Academic and scientific offices
Elfving graduated from the University of Helsinki.
During 1938–1945, Elfving worked as a lecturer at the Helsinki University of Technology.
During the academic year 1946–1947, Elfving served as locum tenens professor at Stockholm University. In 1948 Elfving became a Professor of Mathematics at the University of Helsinki succeeding Lars Ahlfors, who had moved to Harvard University. Elfving visited William Feller at Cornell University in 1949 and 1950. He was an invited plenary speaker at the Third Berkeley Symposium on Probability and Mathematical Statistics in 1955. That same year, he visited Columbia University in the Spring, at the invitation of Theodore W. Anderson, Herbert Robbins, and Herbert Solomon. He visited Solomon again at Stanford University during the fall of 1960 and the spring of 1966.[1]
At the University of Helsinki from 1964 to 1975, Elfving acted as the "inspector" of the Åbo Nation, a Swedish-speaking"nation" at the University of Helsinki.[19] In Finnish and Swedish universities, "nations" are student associations with similarities to fraternities or cooperatives; the inspector is a highly respected university officer, usually a senior professor, who officiates and delivers addresses at formal functions.
Elfving, G. (1959). "Design of linear experiments". In Grenander, Ulf (ed.). Probability and statistics: The Harald Cramér volume. Almqvist & Wiksell, Stockholm; John Wiley & Sons, New York. pp. 58–74. MR0111106.
Elfving, Gustav (1981). The history of mathematics in Finland 1828–1918. Helsinki: Societas Scientarium Fennica.
Elfving, G. (1954a). A unified approach to the allocation problem in sampling theory. Abstract from Proc. Inter. Math. Congr., Amsterdam, Sept. 1954.
Elfving, G (1954b). "Geometric allocation theory". Skandinavisk Aktuarietidskrift. 37: 170–190.
Elfving, G. (1956). Selection of nonrepeatable observations for estimation. Proc. Third Berkeley Symp. Math. Statist. Probab volume 1 pp. 69–75. Univ. California Press, Berkeley.
^Rosenqvist, G., Juselius, K., Nordström, K. and Palmgren, J. (eds.) "A Spectrum of Statistical Thought. Essays in Statistical Theory, Economics and Population Genetics in Honour of Johan Fellman", Publications of the Swedish School of Economics and Business Administration, 46, 1991
Draper, Norman R.; Mäkeläinen, Timo; Nordström, Kenneth; Pukelsheim, Friedrich (1999). "Gustav Elfving: An appreciation". In Alho, Juha (ed.). Statistics, registries, and science: Experiences from Finland. Statistics Finland. pp. 123–152. ISBN978-951-727-643-6.
Mäkeläinen, T (1984). "Gustav Elfving". Arkhimedes. 36: 201–208.
Mäkeläinen, T. (1997). Elfving, Gustav. In Leading Personalities in Statistical Sciences: From the Seventeenth Century to the Present (N. L. Johnson and S. Kotz, eds.) 96–98. Wiley-Interscience, New York.
