Wassily Hoeffding was an American

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...

 and probabilist

Probabilist

A probabilist is either:* A follower of probabilism * A mathematician who practices probability theory; see List of mathematical probabilists...

. Hoeffding was one of the founders of nonparametric statistics, in which Hoeffding contributed the idea and basic results on U-statistics.

In 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...

, Hoeffding's inequality

Hoeffding's inequality

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. Hoeffding's inequality was proved by Wassily Hoeffding.LetX_1, \dots, X_n \!...

 provides an upper bound

Upper bound

In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is lesser than or equal to every element of S...

 on the probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 for the sum of random variables to deviate from its expected value

Expected value

In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...

.

Work

In 1948, he introduced the concept of U-statistic

U-statistic

In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory. In elementary statistics, U-statistics arise naturally in producing minimum-variance unbiased estimators...

s.

See the collected works of Wassily Hoeffding.

Writings

• Masstabinvariante Korrelationstheorie, 1940
• On the distribution of the rank correlation coefficient t when the variates are not independent in Biometrika
  Biometrika
  - External links :* . The Internet Archive. 2011....
  
  , 1947
• A class of statistics with a symptotically normal distribution, 1948
• A nonparametric test for independence, 1948
• The central limit theorem for dependent random variables (with 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...
  
  ), 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 Jack 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

• Hoeffding bounds
• Hoeffding C1 statistic
• Hoeffding decomposition
• Hoeffding's independence test
• Hoeffding's inequality
  Hoeffding's inequality
  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. Hoeffding's inequality was proved by Wassily Hoeffding.LetX_1, \dots, X_n \!...
  
  
• Hoeffding-Blum-Kiefer-Rosenblatt process
• Terry-Hoeffding test

External links

• http://www.nap.edu/openbook.php?record_id=11429&page=208 - a biography