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Jaroslav Hájek
Jaroslav Hájek (; 1926–1974) was a Czech mathematician who worked in theoretical and nonparametric statistics. The Hajek projection and the Hájek–Le Cam convolution theorem are named for him (as well as collaborator Lucien Le Cam). Life Jaroslav Hájek studied statistical and insurance engineering at the Faculty of Special Sciences of the Czech Technical University Czech Technical University in Prague (CTU, cs, České vysoké učení technické v Praze, ČVUT) is one of the largest universities in the Czech Republic with 8 faculties, and is one of the oldest institutes of technology in Central Europe. It ... in Prague and in 1950 he successfully completed this study by obtaining an engineering degree. In 1955 he received the title of CSc. for the paper Contributions to the theory of statistical estimation, the supervisor of this thesis was Josef Novák. In 1963, he received a D.Sc. in the same year he received his habilitation at the Faculty of Mathematics and Physics of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Czech People
The Czechs ( cs, Češi, ; singular Czech, masculine: ''Čech'' , singular feminine: ''Češka'' ), or the Czech people (), are a West Slavic ethnic group and a nation native to the Czech Republic in Central Europe, who share a common ancestry, culture, history, and the Czech language. Ethnic Czechs were called Bohemians in English until the early 20th century, referring to the former name of their country, Bohemia, which in turn was adapted from the late Iron Age tribe of Celtic Boii. During the Migration Period, West Slavic tribes settled in the area, "assimilated the remaining Celtic and Germanic populations", and formed a principality in the 9th century, which was initially part of Great Moravia, in form of Duchy of Bohemia and later Kingdom of Bohemia, the predecessors of the modern republic. The Czech diaspora is found in notable numbers in the United States, Canada, Israel, Austria, Germany, Slovakia, Ukraine, Switzerland, Italy, the United Kingdom, Australia, France, Rus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Statistics
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures. Apart from philosophical considerations about how to make statistical inferences and decisions, much of statistical theory consists of mathematical statistics, and is closely linked to probability theory, to utility theory, and to optimization. Scope Statistical theory provides an underlying rationale and provides a consistent basis for the choice of methodology used in ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 distribution-free or having a specified distribution but with the distribution's parameters unspecified. Nonparametric statistics includes both descriptive statistics and statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are violated. Definitions The term "nonparametric statistics" has been imprecisely defined in the following two ways, among others: Applications and purpose Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hajek Projection
In statistics, Hájek projection of a random variable T on a set of independent random vectors X_1,\dots,X_n is a particular measurable function of X_1,\dots,X_n that, loosely speaking, captures the variation of T in an optimal way. It is named after the Czech statistician Jaroslav Hájek . Definition Given a random variable T and a set of independent random vectors X_1,\dots,X_n, the Hájek projection \hat of T onto \ is given by : \hat = \operatorname(T) + \sum_^n \left \operatorname(T\mid X_i) - \operatorname(T)\right= \sum_^n \operatorname(T\mid X_i) - (n-1)\operatorname(T) Properties * Hájek projection \hat is an L^2projection of T onto a linear subspace of all random variables of the form \sum_^n g_i(X_i), where g_i:\mathbb^d \to \mathbb are arbitrary measurable functions such that \operatorname(g_i^2(X_i))<\infty for all * and hence |
Hájek–Le Cam Convolution Theorem
In statistics, the Hájek–Le Cam convolution theorem states that any regular estimator in a parametric model is asymptotically equivalent to a sum of two independent random variables, one of which is normal with asymptotic variance equal to the inverse of Fisher information, and the other having arbitrary distribution. The obvious corollary from this theorem is that the “best” among regular estimators are those with the second component identically equal to zero. Such estimators are called efficient and are known to always exist for regular parametric models. The theorem is named after Jaroslav Hájek and Lucien Le Cam. Statement Let ℘ = be a regular parametric model, and ''q''(''θ''): Θ → ℝ''m'' be a parameter in this model (typically a parameter is just one of the components of vector ''θ''). Assume that function ''q'' is differentiable on Θ, with the ''m × k'' matrix of derivatives denoted as ''q̇θ''. Define : I_^ = \dot(\theta)I^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lucien Le Cam
Lucien Marie Le Cam (November 18, 1924 – April 25, 2000) was a mathematician and statistician. Biography Le Cam was born November 18, 1924 in Croze, France. His parents were farmers, and unable to afford higher education for him; his father died when he was 13. After graduating from a Catholic school in 1942, he began studying at a seminary in Limoges, but immediately quit upon learning that he would not be allowed to study chemistry there. Instead he continued his studies at a lycée, which did not teach chemistry but did teach mathematics. In May 1944 he joined an underground group, and then went into hiding, returning to his school the following November but soon afterwards moving to Paris, where he began studying at the University of Paris. He graduated in 1945 with the degree ''Licence ès Sciences''.. Le Cam then worked for a hydroelectric utility for five years, while meeting at the University of Paris for a weekly seminar in statistics. In 1950, he was invited to become ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Czech Technical University In Prague
Czech Technical University in Prague (CTU, cs, České vysoké učení technické v Praze, ČVUT) is one of the largest university, universities in the Czech Republic with 8 faculties, and is one of the oldest institutes of technology in Central Europe. It is also the oldest non-military technical university in Europe. In the academic year 2020/21, Czech Technical University offered 130 degree programs in Czech and 84 in English. It was considered one of the top 10 universities in emerging Europe and Central Asia in the same year. History It was established as the Institute of Engineering Education in 1707, but as a secondary education (high school) instead of a Tertiary education, tertiary university, by Emperor Joseph I as a response to Christian Josef Willenberg's petition addressed to preceding emperor Leopold I, Holy Roman Emperor, Leopold I. In 1806, the institute of Engineering Education was transformed into Prague Polytechnical Institute (or Prague Polytechnic), when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Czech Statisticians
Czech may refer to: * Anything from or related to the Czech Republic, a country in Europe ** Czech language ** Czechs, the people of the area ** Czech culture ** Czech cuisine * One of three mythical brothers, Lech, Czech, and Rus' Places *Czech, Łódź Voivodeship, Poland *Czechville, Wisconsin, unincorporated community, United States People * Bronisław Czech (1908–1944), Polish sportsman and artist * Danuta Czech (1922–2004), Polish Holocaust historian * Hermann Czech (born 1936), Austrian architect * Mirosław Czech (born 1968), Polish politician and journalist of Ukrainian origin * Zbigniew Czech (born 1970), Polish diplomat See also * Čech, a surname * Czech lands * Czechoslovakia * List of Czechs * * * Czechoslovak (other) * Czech Republic (other) * Czechia (other) Czechia is the official short form name of the Czech Republic. Czechia may also refer to: * Historical Czech lands *Czechoslovakia (1918–1993) *Czech Socialist Republi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Czechoslovak Mathematicians
Czechoslovak may refer to: *A demonym or adjective pertaining to Czechoslovakia (1918–93) **First Czechoslovak Republic (1918–38) ** Second Czechoslovak Republic (1938–39) **Third Czechoslovak Republic (1948–60) **Fourth Czechoslovak Republic (1960–89) **Fifth Czechoslovak Republic (1989–93) *''Czechoslovak'', also ''Czecho-Slovak'', any grouping of the Czech and Slovak ethnicities: **As a national identity, see Czechoslovakism **The title of Symphony no. 8 in G Major op. 88 by Antonín Dvořák in 1889/90 *The Czech–Slovak languages, a West Slavic dialect continuum **The Czechoslovak language, a theoretical standardized form defined as the state language of Czechoslovakia in its Constitution of 1920 **Comparison of Czech and Slovak See also * Slovak Republic (other) * Czech Republic (other) * Czechia (other) * Slovak (other) * Czech (other) Czech may refer to: * Anything from or related to the Czech Republic, a count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1926 Births
Events January * January 3 – Theodoros Pangalos (general), Theodoros Pangalos declares himself dictator in Greece. * January 8 **Abdul-Aziz ibn Saud is crowned King of Kingdom of Hejaz, Hejaz. ** Bảo Đại, Crown Prince Nguyễn Phúc Vĩnh Thuy ascends the throne, the last monarch of Vietnam. * January 12 – Freeman Gosden and Charles Correll premiere their radio program ''Sam 'n' Henry'', in which the two white performers portray two black characters from Harlem looking to strike it rich in the big city (it is a precursor to Gosden and Correll's more popular later program, ''Amos 'n' Andy''). * January 16 – A BBC comic radio play broadcast by Ronald Knox, about a workers' revolution, causes a panic in London. * January 21 – The Belgian Parliament accepts the Locarno Treaties. * January 26 – Scottish inventor John Logie Baird demonstrates a mechanical television system at his London laboratory for members of the Royal Institution and a report ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1974 Deaths
Major events in 1974 include the aftermath of the 1973 oil crisis and the resignation of President of the United States, United States President Richard Nixon following the Watergate scandal. In the Middle East, the aftermath of the 1973 Yom Kippur War determined politics; following List of Prime Ministers of Israel, Israeli Prime Minister Golda Meir's resignation in response to high Israeli casualties, she was succeeded by Yitzhak Rabin. In Europe, the Turkish invasion of Cyprus, invasion and occupation of northern Cyprus by Turkey, Turkish troops initiated the Cyprus dispute, the Carnation Revolution took place in Portugal, and Chancellor of Germany, Chancellor of West Germany Willy Brandt resigned following an Guillaume affair, espionage scandal surrounding his secretary Günter Guillaume. In sports, the year was primarily dominated by the 1974 FIFA World Cup, FIFA World Cup in West Germany, in which the Germany national football team, German national team won the championshi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
