Gábor J. Székely
Encyclopedia
Gábor J. Székely (ˈseːkɛj, born February 4, 1947 in Budapest) is a Hungarian-American
statistician
/mathematician
best known for introducing E-statistics or energy statistics [see E-statistics or Package energy in R (programming language)
], e.g. the distance correlation
which is a bona fide dependence measure, equals zero exactly when the variables are independent, the distance skewness
which equals zero exactly when the probability distribution is diagonally symmetric, the E-statistic for normality test
and the E-statistic for clustering. Other important discoveries include the Hungarian semigroups, the location testing for Gaussian scale mixture distributions
, the uncertainty principle
of game theory, the half-coin which involves negative probability
, and the solution of an old open problem of lottery mathematics
: in a 5-from-90 lotto the minimum number of tickets one needs to buy to guarantee that at least one of these tickets has (at least) 2 matches is exactly 100.
graduating in 1970. His first advisor was Alfréd Rényi
. Székely received his Ph.D. in 1971 from Eötvös Loránd University, the Candidate Degree in 1976 under the direction of Paul Erdős
and Andrey Kolmogorov
, and the Doctor of Science
degree from the Hungarian Academy of Sciences
in 1986.
Between 1985 and 1995 Székely was the first program manager of the Budapest Semesters in Mathematics
. Between 1990 and 1997 he was the founding chair of the Department of Stochastics of the Budapest Institute of Technology (Technical University of Budapest) and editor-in-chief of Matematikai Lapok, the official journal of the János Bolyai Mathematical Society
. In 1989 Székely was visiting professor at Yale University
, and in 1990-91 he was the first Lukacs Distinguished Professor
in Ohio. Székely was academic advisor of Morgan Stanley
, NY, and Bunge
, Chicago
, helped to establish the Morgan Stanley Mathematical Modeling Centre in Budapest (2005) and the Bunge Mathematical Institute (BMI) in Warsaw
(2006) to provide quantitative analysis to support the firms' global business. Since 2006 he is a Program Director of Statistics of the National Science Foundation
. Székely is also Research Fellow of the Rényi Institute of Mathematics of the Hungarian Academy of Sciences
and the author of two monographs, Paradoxes of Probability Theory and Mathematical Statistics, and Algebraic Probability Theory (with Imre Z. Ruzsa
).
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
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...
/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....
best known for introducing E-statistics or energy statistics [see E-statistics or Package energy in R (programming language)
R (programming language)
R is a programming language and software environment for statistical computing and graphics. The R language is widely used among statisticians for developing statistical software, and R is widely used for statistical software development and data analysis....
], e.g. the distance correlation
Distance correlation
In statistics and in probability theory, distance correlation is a measure of statistical dependence between two random variables or two random vectors of arbitrary, not necessarily equal dimension. Its important property is that this measure of dependence is zero if and only if the random...
which is a bona fide dependence measure, equals zero exactly when the variables are independent, the distance skewness
Skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. The skewness value can be positive or negative, or even undefined...
which equals zero exactly when the probability distribution is diagonally symmetric, the E-statistic for normality test
Normality test
In statistics, normality tests are used to determine whether a data set is well-modeled by a normal distribution or not, or to compute how likely an underlying random variable is to be normally distributed....
and the E-statistic for clustering. Other important discoveries include the Hungarian semigroups, the location testing for Gaussian scale mixture distributions
Location testing for Gaussian scale mixture distributions
In statistics, the topic of location testing for Gaussian scale mixture distributions arises in some particular types of situations where the more standard Student's t-test is inapplicable...
, the uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
of game theory, the half-coin which involves negative probability
Negative probability
In 1942, Paul Dirac wrote a paper "The Physical Interpretation of Quantum Mechanics" where he introduced the concept of negative energies and negative probabilities:...
, and the solution of an old open problem of lottery mathematics
Lottery mathematics
Lottery mathematics is used here to mean the calculation of the probabilities in a lottery game. The lottery game used in the examples below is one in which one selects 6 numbers from 49, and hopes that as many of those 6 as possible match the 6 that are randomly selected from the same pool of 49...
: in a 5-from-90 lotto the minimum number of tickets one needs to buy to guarantee that at least one of these tickets has (at least) 2 matches is exactly 100.
Life and career
Székely attended the Eötvös Loránd University, HungaryHungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
graduating in 1970. His first advisor was Alfréd Rényi
Alfréd Rényi
Alfréd Rényi was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory.-Life:...
. Székely received his Ph.D. in 1971 from Eötvös Loránd University, the Candidate Degree in 1976 under the direction of Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
and Andrey Kolmogorov
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
, and the Doctor of Science
Doctor of Science
Doctor of Science , usually abbreviated Sc.D., D.Sc., S.D. or Dr.Sc., is an academic research degree awarded in a number of countries throughout the world. In some countries Doctor of Science is the name used for the standard doctorate in the sciences, elsewhere the Sc.D...
degree from the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
in 1986.
Between 1985 and 1995 Székely was the first program manager of the Budapest Semesters in Mathematics
Budapest Semesters in Mathematics
The Budapest Semesters in Mathematics program is a study abroad opportunity for North American undergraduate students in Budapest, Hungary. The coursework is primarily mathematical and conducted in English by Hungarian professors, drawn primarily from Eötvös Loránd University and the Mathematics...
. Between 1990 and 1997 he was the founding chair of the Department of Stochastics of the Budapest Institute of Technology (Technical University of Budapest) and editor-in-chief of Matematikai Lapok, the official journal of the János Bolyai Mathematical Society
János Bolyai Mathematical Society
The János Bolyai Mathematical Society is the Hungarian mathematical society, named after János Bolyai, a 19th century Hungarian mathematician, a co-discoverer of non-Euclidean geometry. It is the professional society of the Hungarian mathematicians, applied mathematicians, and mathematics teachers...
. In 1989 Székely was visiting professor at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
, and in 1990-91 he was the first Lukacs Distinguished Professor
Lukacs Distinguished Professor
The Lukacs Distinguished Professor chair was established in 1989 by The Department of Mathematics and Statistics at Bowling Green State University in honor of Eugene Lukacs, who came to Bowling Green with his colleagues Radha Laha and Vijay Rohatgi in 1972 to establish the doctoral program in...
in Ohio. Székely was academic advisor of Morgan Stanley
Morgan Stanley
Morgan Stanley is a global financial services firm headquartered in New York City serving a diversified group of corporations, governments, financial institutions, and individuals. Morgan Stanley also operates in 36 countries around the world, with over 600 offices and a workforce of over 60,000....
, NY, and Bunge
Bunge Limited
Bunge Limited is a Bermudan food conglomerate with its headquarters in White Plains, New York. As well as being a leading global soybean exporter it is also involved in food processing, grain trading, and fertilizer...
, Chicago
Chicago
Chicago is the largest city in the US state of Illinois. With nearly 2.7 million residents, it is the most populous city in the Midwestern United States and the third most populous in the US, after New York City and Los Angeles...
, helped to establish the Morgan Stanley Mathematical Modeling Centre in Budapest (2005) and the Bunge Mathematical Institute (BMI) in Warsaw
Warsaw
Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...
(2006) to provide quantitative analysis to support the firms' global business. Since 2006 he is a Program Director of Statistics of the National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
. Székely is also Research Fellow of the Rényi Institute of Mathematics of the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
and the author of two monographs, Paradoxes of Probability Theory and Mathematical Statistics, and Algebraic Probability Theory (with Imre Z. Ruzsa
Imre Z. Ruzsa
Imre Z. Ruzsa is a Hungarian mathematician specializing in number theory.Ruzsa participated in the International Mathematical Olympiad for Hungary, winning a silver medal in 1969, and two consecutive gold medals with perfect scores in 1970 and 1971. He graduated from the Eötvös Loránd University...
).
Awards
- Rollo Davidson Prize of Cambridge University (1988)
- Elected Fellow of the International Statistical InstituteInternational Statistical InstituteThe 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...
(1996) - Elected Fellow of the American Statistical AssociationAmerican Statistical AssociationThe American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
(2000) - Elected Fellow of the Institute of Mathematical StatisticsInstitute of Mathematical StatisticsThe 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...
(2010)
Works
- Székely, G. J. (1986) Paradoxes in Probability Theory and Mathematical Statistics, Reidel.
- Ruzsa, I. Z.Imre Z. RuzsaImre Z. Ruzsa is a Hungarian mathematician specializing in number theory.Ruzsa participated in the International Mathematical Olympiad for Hungary, winning a silver medal in 1969, and two consecutive gold medals with perfect scores in 1970 and 1971. He graduated from the Eötvös Loránd University...
and Székely, G. J. (1988) Algebraic Probability Theory, Wiley. - Székely, G. J. (editor) (1995) Contests in Higher Mathematics, Springer.
- Székely, G. J. (1981–82) Why is 7 a mystical number? (in Hungarian) in: MIOK Évkönyv, 482-487, ed. Sándor ScheiberSándor ScheiberSándor Scheiber was a Hungarian rabbi and an eminent Jewish scholar. From 1950 until his death he was director of the Rabbinical Seminary in Budapest.- Biography :...
. - Székely, G.J. and Ruzsa, I.Z. (1982) Intersections of traces of random walks with fixed sets, Annals of Probability 10, 132-136.
- Székely, G. J. and Ruzsa, I.Z. (1985) No distribution is prime, Z. Wahrscheinlichkeitstheorie verw. Geb. 70, 263-269.
- Székely, G. J. and Buczolich, Z. (1989) When is a weighted average of ordered sample elements a maximum likelihood estimator of the location parameter? Advances in Applied Mathematics 10, 439-456.
- Székely, G. J, Bennett, C.D., and Glass, A. M. W. (2004) Fermat's last theoremFermat's Last TheoremIn number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
for rational exponents, The American Mathematical Monthly 11/4, 322-329. - Székely, G. J. (2006) Student's t-test for scale mixtures. Lecture Notes Monograph Series 49, Institute of Mathematical Statistics, 10-18.
- Székely, G. J., Rizzo, M. L. and Bakirov, N. K. (2007) Measuring and testing independence by correlation of distances, The Annals of Statistics, 35, 2769-2794.PDF
- Székely, G. J. and Rizzo, M.L. (2009) Brownian distance covariance, The Annals of Applied Statistics, 3/4, 1233-1308.PDF
- Rizzo, M. L. and Székely, G. J. (2010) DISCO analysis: A nonparametric extension of analysis of variance, The Annals of Applied Statistics, 4/2, 1034-1055.PDF
External links
- Székely's website.
- Gábor J. Székely at the Mathematics Genealogy ProjectMathematics Genealogy ProjectThe Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...