Gustav Elfving
Encyclopedia
Gustav Elfving was a Finnish
mathematician
and statistician
. In statistics, he wrote pioneering papers about the optimal design
of experiments
. He made other notable contributions to the mathematical sciences
and to Finnish universities.
, and Thyra Elfving (née Ingman). He was the youngest of four children. Gustav Elfving earned excellent grades at the Svenska normallyceum, a Helsinki gymnasium for Swedish-speaking boys, from which he graduated in 1926. In the same year he enrolled at the University of Helsinki, planning to major in astronomy. He switched to mathematics, graduating in 1930 in mathematics, with astronomy and physics as minor subjects. During 1927–1929, he worked as a computational assistant at the astronomical observatory of
the University of Helsinki. He studied probability theory
under J. W. Lindeberg
, who is now known for Lindeberg's condition
for the central limit theorem
. He wrote his (1934) dissertation under the supervision of Rolf Nevanlinna
; his thesis studied Riemann surfaces and their uniformization
. In the Nevalinna theory
of the values of meromorphic function
s, Elfving's results were praised by Drasin.
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. Elfving was photographed while he made theodolite
measurements and peered from a tent. 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.
, Elfving did research in the design of experiments
, probability theory
, and statistical inference
, as well as applications.
, including "Elfving sets" and Elfving's theorem. Being symmetric, Elfving sets are formed by the union of a set and its reflection through the origin, −S ∪ S. According to , 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acknowledged unpublished notes of L. J. Savage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
.
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
. Elfving introduced the statistical symbol for probabilistic independence ⊥⊥, which is a stronger condition than orthogonality
⊥, by the 1950s.
Elfving made notable contributions in many fields. In mathematics, he did research in complex analysis
and probability theory (particularly Markov
and point process
es). In statistical theory, his most influential work was in optimal design, but he also worked in sampling theory
,
psychometrics
, applied statistics, and the decision sciences (including decision theory
, game theory
, and Bayesian statistics
). He also contributed to mathematics education
by writing textbooks, book reviews, and popular science
. He wrote papers and a book on the history of mathematics
.
succeeding Lars Ahlfors, who had moved to Harvard University. During the academic year 1946–1947, Elfving served as locum tenens professor at Stockholm University. Elfving visited William Feller
at Cornell University
during 1949–1950. 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.
He was elected as a fellow of the Institute of Mathematical Statistics
in 1955 and an elected member of the International Statistical Institute
in 1963. Elfving was elected as a foreign member of the Swedish Academy of Sciences in 1974, the same year that he was elected to the Royal Statistical Society
. He served on the editorial boards of three international journals: Probability Theory and Related Fields
(1962–1975), The Annals of Mathematical Statistics
(1964–1967), and Mathematica Scandinavica (1953–1972). Elfving had a deep sense of honor and propriety: When he resigned from the editorial boards following decades of service, he requested that he not be sent complimentary issues of the journals; when he failed to accomplish high levels of research, he offered to return the funding to the granting agency.
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. 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.
Finland
Finland , officially the Republic of Finland, is a Nordic country situated in the Fennoscandian region of Northern Europe. It is bordered by Sweden in the west, Norway in the north and Russia in the east, while Estonia lies to its south across the Gulf of Finland.Around 5.4 million people reside...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
. In statistics, he wrote pioneering papers about the optimal design
Optimal design
Optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion.In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance...
of experiments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
. He made other notable contributions to the mathematical sciences
Mathematical sciences
Mathematical sciences is a broad term that refers to those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper...
and to Finnish universities.
Early life
Erik Gustav Elfving was son of Frederik Elfving, a professor of botany at the University of HelsinkiUniversity of Helsinki
The University of Helsinki is a university located in Helsinki, Finland since 1829, but was founded in the city of Turku in 1640 as The Royal Academy of Turku, at that time part of the Swedish Empire. It is the oldest and largest university in Finland with the widest range of disciplines available...
, and Thyra Elfving (née Ingman). He was the youngest of four children. Gustav Elfving earned excellent grades at the Svenska normallyceum, a Helsinki gymnasium for Swedish-speaking boys, from which he graduated in 1926. In the same year he enrolled at the University of Helsinki, planning to major in astronomy. He switched to mathematics, graduating in 1930 in mathematics, with astronomy and physics as minor subjects. During 1927–1929, he worked as a computational assistant at the astronomical observatory of
the University of Helsinki. He studied probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
under J. W. Lindeberg
Jarl Waldemar Lindeberg
Jarl Waldemar Lindeberg was a Finnish mathematician known for work on the central limit theorem....
, who is now known for Lindeberg's condition
Lindeberg's condition
In probability theory, Lindeberg's condition is a sufficient condition for the central limit theorem to hold for a sequence of independent random variables...
for the central limit theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
. He wrote his (1934) dissertation under the supervision of Rolf Nevanlinna
Rolf Nevanlinna
Rolf Herman Nevanlinna was one of the most famous Finnish mathematicians. He was particularly appreciated for his work in complex analysis.- The Nevanlinna family :...
; his thesis studied Riemann surfaces and their uniformization
Uniformization theorem
In mathematics, the uniformization theorem says that any simply connected Riemann surface is conformally equivalent to one of the three domains: the open unit disk, the complex plane, or the Riemann sphere. In particular it admits a Riemannian metric of constant curvature...
. In the Nevalinna theory
Value distribution theory of holomorphic functions
In mathematics, the value distribution theory of holomorphic functions is a division of mathematical analysis. It tries to get quantitative measures of the number of times a function f assumes a value a, as z grows in size, refining the Picard theorem on behaviour close to an essential singularity...
of the values of meromorphic function
Meromorphic function
In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function...
s, Elfving's results were praised by Drasin.
Fiancée's death and his 1935 expedition to Greenland
Tuberculosis
Tuberculosis, MTB, or TB is a common, and in many cases lethal, infectious disease caused by various strains of mycobacteria, usually Mycobacterium tuberculosis. Tuberculosis usually attacks the lungs but can also affect other parts of the body...
. 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. Elfving was photographed while he made theodolite
Theodolite
A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...
measurements and peered from a tent. 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
Least squares
The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...
estimation.
Statistical research
In statisticsStatistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, Elfving did research in the design of experiments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
, probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, and statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
, as well as applications.
Optimal design of experiments
In statistics, Elfving is known as one of the founders of the modern theory of the optimal design of experiments. While accompanying a surveying expedition to western Greenland, extended and intense rains left Elving with three days in his tent, during which time he consider the best locations of observations to estimate parameters on linear models. Elfving's ideas appeared in his paper on the optimal design of experiments for estimating linear models. This paper also introduced concepts from convex geometryConvex geometry
Convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming,...
, including "Elfving sets" and Elfving's theorem. Being symmetric, Elfving sets are formed by the union of a set and its reflection through the origin, −S ∪ S. According to , Elfving was generous in crediting others' results: His paper in the Cramér
Harald Cramér
Harald Cramér was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. He was once described by John Kingman as "one of the giants of statistical theory".-Early life:Harald Cramér was born in Stockholm, Sweden on September...
-festschrift
Festschrift
In academia, a Festschrift , is a book honoring a respected person, especially an academic, and presented during his or her lifetime. The term, borrowed from German, could be translated as celebration publication or celebratory writing...
acknowledged unpublished notes of L. J. Savage
Leonard Jimmie Savage
Leonard Jimmie Savage was an American mathematician and statistician. Nobel Prize-winning economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius."...
; Elfving was a referee for the fundamental paper on optimal designs by Kiefer and Wolfowitz
Jacob Wolfowitz
Jacob Wolfowitz was a Polish-born American statistician and Shannon Award-winning information theorist. He was the father of former Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz....
.
Other statistical contributions
As a Professor at the University of Helsinki, Elfving was responsible for writing Finnish languageFinnish language
Finnish is the language spoken by the majority of the population in Finland Primarily for use by restaurant menus and by ethnic Finns outside Finland. It is one of the two official languages of Finland and an official minority language in Sweden. In Sweden, both standard Finnish and Meänkieli, a...
texts, which were used for decades. In his texts and reviews, Elfving emphasized the decision-theoretic foundations of statistics, following Neyman
Jerzy Neyman
Jerzy Neyman , born Jerzy Spława-Neyman, was a Polish American mathematician and statistician who spent most of his professional career at the University of California, Berkeley.-Life and career:...
, Pearson
Egon Pearson
Egon Sharpe Pearson, CBE FRS was the only son of Karl Pearson, and like his father, a leading British statistician....
, and Wald
Abraham Wald
- See also :* Sequential probability ratio test * Wald distribution* Wald–Wolfowitz runs test...
, and recognized the value of Bayesian methods
Bayesian statistics
Bayesian statistics is that subset of the entire field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities...
in statistics and also in operations research
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
. Elfving introduced the statistical symbol for probabilistic independence ⊥⊥, which is a stronger condition than orthogonality
Orthogonality
Orthogonality occurs when two things can vary independently, they are uncorrelated, or they are perpendicular.-Mathematics:In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle...
⊥, by the 1950s.
Elfving made notable contributions in many fields. In mathematics, he did research in complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
and probability theory (particularly Markov
Markov process
In probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds...
and point process
Point process
In statistics and probability theory, a point process is a type of random process for which any one realisation consists of a set of isolated points either in time or geographical space, or in even more general spaces...
es). In statistical theory, his most influential work was in optimal design, but he also worked in sampling theory
Sampling theory
sampling theory may mean:* Nyquist–Shannon sampling theorem, digital signal processing * Statistical sampling* Fourier sampling...
,
psychometrics
Psychometrics
Psychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, personality traits, and educational measurement...
, applied statistics, and the decision sciences (including decision theory
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
, game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, and Bayesian statistics
Bayesian statistics
Bayesian statistics is that subset of the entire field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities...
). He also contributed to mathematics education
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
by writing textbooks, book reviews, and popular science
Popular science
Popular science, sometimes called literature of science, is interpretation of science intended for a general audience. While science journalism focuses on recent scientific developments, popular science is broad-ranging, often written by scientists as well as journalists, and is presented in many...
. He wrote papers and a book on the history of mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
.
Students
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. 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.Academic and scientific offices
Elfving became the Professor of Mathematics at the Helsinki University of TechnologyHelsinki University of Technology
Aalto University School of Science and Technology , was the temporary name for Helsinki University of Technology during the process of forming the Aalto University...
succeeding Lars Ahlfors, who had moved to Harvard University. During the academic year 1946–1947, Elfving served as locum tenens professor at Stockholm University. Elfving visited William Feller
William Feller
William Feller born Vilibald Srećko Feller , was a Croatian-American mathematician specializing in probability theory.-Early life and education:...
at Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
during 1949–1950. 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
Herbert Robbins
Herbert Ellis Robbins was an American mathematician and statistician who did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of What is Mathematics?, a popularization that is still in print. The Robbins lemma, used in...
, and Herbert Solomon. He visited Solomon again at Stanford University during the Fall of 1960 and the Spring of 1966.
He was elected as a fellow of the Institute of Mathematical Statistics
Institute of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world...
in 1955 and an elected member of the International Statistical Institute
International Statistical Institute
The International Statistical Institute is a professional association of statisticians. The Institut International de Statistique or International Statistical Institute was founded in 1885 although there had been international congresses from 1853.. The Institute publishes a variety of books and...
in 1963. Elfving was elected as a foreign member of the Swedish Academy of Sciences in 1974, the same year that he was elected to the Royal Statistical Society
Royal Statistical Society
The Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824...
. He served on the editorial boards of three international journals: Probability Theory and Related Fields
Probability Theory and Related Fields
Probability Theory and Related Fields is a peer-reviewed mathematics journal published by Springer.Established in 1962, it was originally named Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, with the English replacing the German starting from volume 71...
(1962–1975), The Annals of Mathematical Statistics
Annals of Mathematical Statistics
The Annals of Mathematical Statistics was a peer-reviewed statistics journal published by the Institute of Mathematical Statistics from 1930 to 1972. It was superseded by the Annals of Statistics and the Annals of Probability.-External links:*...
(1964–1967), and Mathematica Scandinavica (1953–1972). Elfving had a deep sense of honor and propriety: When he resigned from the editorial boards following decades of service, he requested that he not be sent complimentary issues of the journals; when he failed to accomplish high levels of research, he offered to return the funding to the granting agency.
At the University of Helsinki from 1964 to 1975, Elfving acted as the "inspector
Inspektor
Inspektor, Swedish for Inspector, is the largely honorary chairmanship of a student nations in Lund and Uppsala universities in Sweden. The Inspector has a supervisory role his/her nation and presides over most important functions. It is a quite prestigious role to be invited to undertake as it...
" of the Åbo Nation
Åbo Nation
Åbo Nation is one of the 15 student nations at the University of Helsinki, Swedish-speaking and established in 1643....
, a Swedish-speaking "nation" at the University of Helsinki. In Finnish and Swedish universities, "nations"
Nations at Finnish universities
In Finland, student nations are student organisations within which a large proportion of extra-curricular student activity takes place...
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.
External links
- Photograph of Elfving on the Portraits of Statisticians page.
