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Wassily Hoeffding
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. 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. 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, 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 Russ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mukhino, Leningrad Oblast
Mukhino (russian: Му́хино; fi, Mustamäki) is a rural locality on the north-eastern shore of the Roshchinka River, on Karelian Isthmus, in Vyborgsky District of Leningrad Oblast, served by the station 63rd km of the Saint Petersburg–Vyborg Vyborg (; rus, Вы́борг, links=1, r=Výborg, p=ˈvɨbərk; fi, Viipuri ; sv, Viborg ; german: Wiborg ) is a town in, and the administrative center of, Vyborgsky District in Leningrad Oblast, Russia. It lies on the Karelian Isthmus ne ... railroad. Rural localities in Leningrad Oblast Karelian Isthmus {{LeningradOblast-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 estimators. The theory of U-statistics allows a minimum-variance unbiased estimator to be derived from each unbiased estimator of an ''estimable parameter'' (alternatively, ''statistical functional'') for large classes of probability distributions. An estimable parameter is a measurable function of the population's cumulative probability distribution: For example, for every probability distribution, the population median is an estimable parameter. The theory of U-statistics applies to general classes of probability distributions. History Many statistics originally derived for particular parametric families have been recognized as U-statistics for general distributions. In non-parametric statistics, the theory of U-statistics is used to esta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 estimators. The theory of U-statistics allows a minimum-variance unbiased estimator to be derived from each unbiased estimator of an ''estimable parameter'' (alternatively, ''statistical functional'') for large classes of probability distributions. An estimable parameter is a measurable function of the population's cumulative probability distribution: For example, for every probability distribution, the population median is an estimable parameter. The theory of U-statistics applies to general classes of probability distributions. History Many statistics originally derived for particular parametric families have been recognized as U-statistics for general distributions. In non-parametric statistics, the theory of U-statistics is used to esta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Humboldt 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 of Wilhelm von Humboldt, Johann Gottlieb Fichte and Friedrich Ernst Daniel Schleiermacher as the University of Berlin () in 1809, and opened in 1810, making it the oldest of Berlin's four universities. From 1828 until its closure in 1945, it was named Friedrich Wilhelm University (german: Friedrich-Wilhelms-Universität). During the Cold War, the university found itself in East Berlin and was ''de facto'' split in two when the Free University of Berlin opened in West Berlin. The university received its current name in honour of Alexander and Wilhelm von Humboldt in 1949. The university is divided into nine faculties including its medical school shared with the Freie Universität Berlin. The university has a student enrollment of around 32 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 influenced by Søren Kierkegaard in his early development, but later became a positivist, retaining and combining with it the spirit and method of practical psychology and the critical school. The physicist Niels Bohr studied philosophy from and became a friend of Høffding. The philosopher and author Ágúst H. Bjarnason was a student of Høffding. Høffding's great-nephew was the statistician Wassily Hoeffding. Høffding died in Copenhagen. Work His best-known work is perhaps his ''Den nyere Filosofis Historie'' (1894), translated into English from the German edition (1895) by B.E. Meyer as ''History of Modern Philosophy'' (2 vols., 1900), a work intended by him to supplement and correct that of Hans Brøchner, to whom it is dedicated. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Danish People
Danes ( da, danskere, ) are a North Germanic ethnic group and nationality native to Denmark and a modern nation identified with the country of Denmark. This connection may be ancestral, legal, historical, or cultural. Danes generally regard themselves as a nationality and reserve the word "ethnic" for the description of recent immigrants, sometimes referred to as "new Danes". The contemporary Danish national identity is based on the idea of "Danishness", which is founded on principles formed through historical cultural connections and is typically not based on racial heritage. History Early history Denmark has been inhabited by various Germanic peoples since ancient times, including the Angles, Cimbri, Jutes, Herules, Teutones and others. The first mentions of " Danes" are recorded in the mid-6th century by historians Procopius ( el, δάνοι) and Jordanes (''danī''), who both refer to a tribe related to the Suetidi inhabiting the peninsula of Jutland, the province of Sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Berngardovich Struve
Peter (or Pyotr or Petr) Berngardovich Struve (russian: Пётр Бернга́рдович Стру́ве; pronounced ; 26 January 1870 in Perm – 22 February 1944 in Paris) was a Russian political economist, philosopher, historian and editor. He started out as a Marxist, later became a liberal and after the Bolshevik Revolution joined the White movement. From 1920, he lived in exile in Paris, where he was a prominent critic of Russian Communism. Biography Marxist theoretician Peter Struve is probably the best known member of the Russian branch of the Struve family. Son of Bernhard Struve (Astrakhan and later Perm governor) and grandson of astronomer Friedrich Georg Wilhelm von Struve, he entered the Natural Sciences Department of the University of Saint Petersburg in 1889 and transferred to its law school in 1890. While there, he became interested in Marxism, attended Marxist and narodniki (populist) meetings (where he met his future opponent Vladimir Lenin) and wrote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The American Statistical Association
The ''Journal of the American Statistical Association (JASA)'' is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States. It is published four times a year in March, June, September and December by Taylor & Francis, Ltd on behalf of the American Statistical Association. As a statistics journal it publishes articles primarily focused on the application of statistics, statistical theory and methods in economic, social, physical, engineering, and health sciences. The journal also includes reviews of academic books which are important to the advancement of the field. It had an impact factor of 2.063 in 2010, tenth highest in the "Statistics and Probability" category of ''Journal Citation Reports''. In a 2003 survey of statisticians, the ''Journal of the American Statistical Association'' was ranked first, among all journals, for "Applications of Statistics" and second (after ''Annals of Statistics'') f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to end th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 possible upper sides of a flipped coin such as heads H and tails T) in a sample space (e.g., the set \) to a measurable space, often the real numbers (e.g., \ in which 1 corresponding to H and -1 corresponding to T). Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup. In the formal mathematical language of measure theory, a random vari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 of that is less than or equal to every element of . A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds. Examples For example, is a lower bound for the set (as a subset of the integers or of the real numbers, etc.), and so is . On the other hand, is not a lower bound for since it is not smaller than every element in . The set has as both an upper bound and a lower bound; all other numbers are either an upper bound or a lower bound for that . Every subset of the natural numbers has a lowe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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