mathematics

Gábor J. Székely

Gábor J. Székely is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Gábor J. Székely rather than just read about it. In short: Gábor J. Székely (Hungarian pronunciation: [ˈseːkɛj]; born February 4, 1947, in Budapest) is a Hungarian-American statistician/mathematician best known for introducing energy statistics (E-statistics).

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Reference excerpt

Gábor J. Székely (Hungarian pronunciation: [ˈseːkɛj]; born February 4, 1947, in Budapest) is a Hungarian-American statistician/mathematician best known for introducing energy statistics (E-statistics). Examples include: 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.

Life and career Székely attended the Eötvös Loránd University, Hungary 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. During the years 1970-1995 he has worked as a Professor in Eötvös Loránd University at the Department of Probability Theory and Statistics. 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. Since 1995 he has been teaching at the Bowling Green State University at the Department of Mathematics and Statistics. 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, now retired. Székely is also Research Fellow of the Rényi Institute of Mathematics of the Hungarian Academy of Sciences. For an informal biographical sketch see Conversations with Gábor J. Székely

Awards Rollo Davidson Prize of Cambridge University (1988) Elected Fellow of the International Statistical Institute (1996) Elected Fellow of the American Statistical Association (2000) Elected Fellow of the Institute of Mathematical Statistics (2010)

Books Székely, G. J. (1986) Paradoxes in Probability Theory and Mathematical Statistics, Reidel. Ruzsa, I. Z. and Székely, G. J. (1988) Algebraic Probability Theory, Wiley. Székely, G. J. (editor) (1995) Contests in Higher Mathematics, Springer. Rao, C.R. and Székely, G.J. (editors) (2000) Statistics For The 21st Century: Methodologies For Applications Of The Future (Statistics, Textbooks And Monographs), New York, Marcel Dekker. Guoyan Zheng, Shuo Li, Székely, G. J.(2017)Statistical Shape and Deformation Analysis, 1st Edition, Academic Press. Székely, G.J. and Rizzo, M.L. (2023) The Energy of Data and Distance Correlation, Chapman and Hall/CRC Press, Monographs on Statistics and Applied Probability Volume 171 [1].

Selected works Székely, G. J. (1981–82) Why is 7 a mystical number? (in Hungarian) in: MIOK Évkönyv, 482-487, ed. Sándor Scheiber. 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. [2] Székely, G. J, Bennett, C.D., and Glass, A. M. W. (2004) Fermat's last theorem 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. arXiv:0803.4101 Székely, G. J. and Rizzo, M.L. (2009) Brownian distance covariance, The Annals of Applied Statistics, 3/4, 1233-1308. arXiv:1010.0297 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. arXiv:1011.2288 Székely, G.J. and Rizzo, M.L. (2013) Energy statistics: statistics based on distances, Invited paper, Journal of Statistical Planning and Inference, 143/8, 1249-1272. Székely, G.J. and Rizzo, M.L. (2014) Partial distance correlation with methods for dissimilarities, The Annals of Statistics, 42/6, 2382-2412.

References

External links Székely's website Archived 2010-11-12 at the Wayback Machine. Gábor J. Székely at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Gábor J. Székely

Start with the simplest possible case. Write down what Gábor J. Székely claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Gábor J. Székely before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Gábor J. Székely ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Gábor J. Székely

In research: Gábor J. Székely appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Gábor J. Székely in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Gábor J. Székely is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, 20th-century Hungarian mathematicians, 20th-century statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Gábor J. Székely outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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Frequently asked questions

What is Gábor J. Székely in simple terms?

Why does Gábor J. Székely matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Gábor J. Székely?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Gábor J. Székely.