Wassily Hoeffding

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Wassily Hoeffding
Born(1914-06-12)June 12, 1914
DiedFebruary 28, 1991(1991-02-28) (aged 76)
Alma materBerlin University
Known forHoeffding's inequality
Scientific career
InstitutionsUniversity of North Carolina at Chapel Hill
Doctoral advisorAlfred Klose
Doctoral students

Wassily Hoeffding (June 12, 1914 – February 28, 1991) was a Finnish statistician and probabilist. Hoeffding was one of the founders of nonparametric statistics, in which Hoeffding contributed the idea and basic results on U-statistics.[1][2]

In probability theory, Hoeffding's inequality provides an upper bound on the probability for the sum of random variables to deviate from its expected value.[3]

Personal life[edit]

Hoeffding was born in Mustamäki, Finland, (Gorkovskoye, Russia since 1940), although his place of birth is registered as St. Petersburg on his birth certificate. His father was an economist and a disciple of Peter Struve, the Russian social scientist and public figure. His paternal grandparents were Danish and his father's uncle was the Danish philosopher Harald Høffding. His mother, née Wedensky, had studied medicine. Both grandfathers had been engineers. In 1918 the family left Tsarskoye Selo for Ukraine and, after traveling through scenes of civil war, finally left Russia for Denmark in 1920, where Wassily entered school.

In 1924 the family settled in Berlin. Hoeffding obtained his PhD in 1940 at the University of Berlin. He migrated with his mother to the United States in 1946. His younger brother, Oleg, became a military historian in the United States. [4]


In 1948, he introduced the concept of U-statistics.

See the collected works of Wassily Hoeffding.[5]


  • Masstabinvariante Korrelationstheorie, 1940
  • On the distribution of the rank correlation coefficient t when the variates are not independent in Biometrika, 1947
  • A class of statistics with asymptotically normal distribution, 1948
  • A nonparametric test for independence, 1948
  • The central limit theorem for dependent random variables (with Herbert Robbins), 1948
  • "Optimum" nonparametric tests, 1951
  • A combinatorial central limit theorem, 1951
  • The large-sample power of test based on permutations of observations, 1952
  • On the distribution of the expected values of the order statistics, 1953
  • The efficiency of tests (with J. R. Rosenblatt), 1955
  • On the distribution of the number of successes in independent trials, 1956
  • Distinguishability of sets of distributions. (The case of independent and identically distributed random variables.), (with Jacob Wolfowitz), 1958
  • Lower bounds for the expected sample size and the average risk of a sequential procedure, 1960
  • Probability inequalities for sums of bounded random variables, 1963

See also[edit]


  1. ^ Wassily Hoeffding (1948) "A class of statistics with asymptotically normal distributions". Annals of Statistics, 19, 293–325. (Partially reprinted in: Kotz, S., Johnson, N.L. (1992) Breakthroughs in Statistics, Vol I, pp 308–334. Springer-Verlag. ISBN 0-387-94037-5)
  2. ^ Sen, P.K (1992) "Introduction to Hoeffding (1948) A Class of Statistics with Asymptotically Normal Distribution". In: Kotz, S., Johnson, N.L. Breakthroughs in Statistics, Vol I, pp 299–307. Springer-Verlag. ISBN 0-387-94037-5.
  3. ^ Wassily Hoeffding (1963) Probability inequalities for sums of bounded random variables, Journal of the American Statistical Association, 58 (301), 13–30. (JSTOR)
  4. ^ Fisher, Nickolas J; van Zwet, Willem R. "Biographic Memoirs Volume 86". The National Academies Press, Washington D.C. Retrieved July 28, 2016.
  5. ^ The Collected Works of Wassily Hoeffding (1994), N. I. Fisher and P. K. Sen, eds., Springer-Verlag, New York.

External links[edit]