Wassily Hoeffding (June 12, 1914 – February 28, 1991) was a

Finnish Finnish may refer to: * Something or someone from, or related to Finland * Culture of Finland * Finnish people or Finns, the primary ethnic group in Finland * Finnish language, the national language of the Finnish people * Finnish cuisine See also ...

statistician A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...

and probabilist. Hoeffding was one of the founders of

nonparametric statistics Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distr ...

, in which Hoeffding contributed the idea and basic results on

U-statistics In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory; the letter "U" stands for unbiased. In elementary statistics, U-statistics arise naturally in producing minimum-variance unbiased est ...

. In

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

Hoeffding's inequality In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was proven by Wassi ...

provides an

upper bound In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of . Dually, a lower bound or minorant of is defined to be an element ...

on the

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

for the sum of

random variables A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...

to deviate from its

expected value In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a l ...

Personal life

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 Peter (or Pyotr or Petr) Berngardovich Struve (russian: Пётр Бернга́рдович Стру́ве; pronounced ; 26 January 1870 in Perm, Russia, Perm – 22 February 1944 in Paris) was a Russian Political economy, political economist, ph ...

, the Russian social scientist and public figure. His paternal grandparents were

Danish Danish may refer to: * Something of, from, or related to the country of Denmark People * A national or citizen of Denmark, also called a "Dane," see Demographics of Denmark * Culture of Denmark * Danish people or Danes, people with a Danish ance ...

and his father's uncle was the Danish philosopher

Harald Høffding Harald Høffding (11 March 1843 – 2 July 1931) was a Danish philosopher and theologian. Life Born and educated in Copenhagen, he became a schoolmaster, and ultimately in 1883 a professor at the University of Copenhagen. He was strongly influe ...

. 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 Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...

. He migrated with his mother to the United States in 1946. His younger brother, Oleg, became a military historian in the United States. Hoeffding's ashes were buried in a small cemetery on land owned by George E. Nicholson, Jr.'s family in Chatham County, NC about 11 miles south of Chapel Hill, NC.

Work

In 1948, he introduced the concept of

U-statistic In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory; the letter "U" stands for unbiased. In elementary statistics, U-statistics arise naturally in producing minimum-variance unbiased est ...

s. See the collected works of Wassily Hoeffding.''The Collected Works of Wassily Hoeffding'' (1994), N. I. Fisher and P. K. Sen, eds., Springer-Verlag, New York.

Writings

* ''Masstabinvariante Korrelationstheorie'', 1940 * ''On the distribution of the rank correlation coefficient t when the variates are not independent'' in

Biometrika ''Biometrika'' is a peer-reviewed scientific journal published by Oxford University Press for thBiometrika Trust The editor-in-chief is Paul Fearnhead (Lancaster University). The principal focus of this journal is theoretical statistics. It was es ...

, 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 Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician. He did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant ...

), 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 Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American Jewish statistician and Shannon Award-winning information theorist. He was the father of former United States Deputy Secretary of Defense and World Bank Group President ...

), 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

References

External links

* {{DEFAULTSORT:Hoeffding, Wassily 1914 births 1991 deaths People from Vyborg District People from Viipuri Province (Grand Duchy of Finland) American people of Danish descent Presidents of the Institute of Mathematical Statistics Fellows of the American Statistical Association American statisticians Probability theorists 20th-century American mathematicians White Russian emigrants to Germany German emigrants to the United States Finnish statisticians