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Èlizbar Nadaraya
Èlizbar Nadaraya is a Georgian mathematician who is currently a Full Professor and the Chair of the Theory of Probability and Mathematical Statistics at the Tbilisi State University. He developed the Nadaraya-Watson estimator along with Geoffrey Watson, which proposes estimating the conditional expectation of a random variable as a locally weighted average using a kernel as a weighting function. Nadaraya was born in 1936 in Khobi, Georgia. He received his doctoral degree from the V.I. Romanovski Institute of Mathematics, Tashkent in 1981. He has since co-authored over 120 publications including 5 textbooks in the area of probability and statistics. Most cited publications Book *E. A. Nadaraya, ''Nonparametric Estimation of Probability Densities and Regression Curves'' Springer, 198Nonparametric Estimation of Probability Densities and Regression CurvesISBN 978-90-277-2757-2 (Cited 319 times, according to Google Scholar.) Journal articles *Nadaraya EA. On estimating regression ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nadaraya-Watson Estimator
In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables ''X'' and ''Y''. In any nonparametric regression, the conditional expectation of a variable Y relative to a variable X may be written: : \operatorname(Y \mid X) = m(X) where m is an unknown function. Nadaraya–Watson kernel regression Nadaraya and Watson, both in 1964, proposed to estimate m as a locally weighted average, using a kernel as a weighting function. The Nadaraya–Watson estimator is: : \widehat_h(x)=\frac where K_h(t) = \fracK\left(\frac\right) is a kernel with a bandwidth h such that K(\cdot) is of order at least 1, that is \int_^\infty u K(u) \, du = 0. Derivation Starting with the definition of conditional expectation, : \operatorname(Y \mid X=x) = \int y f(y\mid x) \, dy = \int y \frac \, dy we estimate the joint distributions ''f''(''x'',''y' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geoffrey Watson
Geoffrey Stuart Watson (3 December 1921 – 3 January 1998) was an Australian statistician. Watson was born in Bendigo, Victoria in 1921. He studied at the University of Melbourne, and received his PhD at the North Carolina State University in 1951. After taking positions at the University of Melbourne, the Australian National University, the University of Toronto and Johns Hopkins University, he became chair of the Department of Statistics of Princeton University in 1970. He remained there until his death. Watson developed the Durbin–Watson statistic for detecting autocorrelation with James Durbin of the London School of Economics in 1950. Watson was especially interested in applications of statistics. He used statistical methods to support the theory of continental drift. He estimated the size of the penguin population in Antarctica, and the effect of repealing the motorcycle helmet law in the United States. In 1966, he was elected as a Fellow of the American Statistical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Expectation
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of those values. More formally, in the case when the random variable is defined over a discrete probability space, the "conditions" are a partition of a set, partition of this probability space. Depending on the context, the conditional expectation can be either a random variable or a function. The random variable is denoted E(X\mid Y) analogously to conditional probability. The function form is either denoted E(X\mid Y=y) or a separate function symbol such as f(y) is introduced with the meaning E(X\mid Y) = f(Y). Examples Example 1: Dice rolling Consider the roll of a fair die and let ''A'' = 1 if the number is even (i.e., 2, 4, or 6) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function (mathematics), function in which * the Domain of a function, domain is the set of possible Outcome (probability), outcomes in a sample space (e.g. the set \ which are the possible upper sides of a flipped coin heads H or tails T as the result from tossing a coin); and * the Range of a function, range is a measurable space (e.g. corresponding to the domain above, the range might be the set \ if say heads H mapped to -1 and T mapped to 1). Typically, the range of a random variable is a subset of the Real number, real numbers. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel (statistics)
The term kernel is used in statistics, statistical analysis to refer to a window function. The term "kernel" has several distinct meanings in different branches of statistics. Bayesian statistics In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the variables in the domain are omitted. Note that such factors may well be functions of the parameters of the pdf or pmf. These factors form part of the normalization factor of the probability distribution, and are unnecessary in many situations. For example, in pseudo-random number sampling, most sampling algorithms ignore the normalization factor. In addition, in Bayesian analysis of conjugate prior distributions, the normalization factors are generally ignored during the calculations, and only the kernel considered. At the end, the form of the kernel is examined, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Khobi
Khobi ( ka, ხობი) is a town in western Georgia with a population of 4,242. The settlement of Khobi acquired the status of a town in 1981 and currently functions as an administrative center of the Khobi District within the Samegrelo-Zemo Svaneti region. See also * Samegrelo-Zemo Svaneti Samegrelo-Zemo Svaneti ( Georgian: სამეგრელო-ზემო სვანეთი ) is a region (Mkhare) in western Georgia with a population of 308,358 (2021) and a surface of . The region has Zugdidi as its administrative center ... References Cities and towns in Samegrelo-Zemo Svaneti {{Georgia-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georgia (country)
Georgia is a country in the Caucasus region on the coast of the Black Sea. It is located at the intersection of Eastern Europe and West Asia, and is today generally regarded as part of Europe. It is bordered to the north and northeast by Russia, to the south by Turkey and Armenia, and to the southeast by Azerbaijan. Georgia covers an area of . It has a Demographics of Georgia (country), population of 3.7 million, of which over a third live in the capital and List of cities and towns in Georgia (country), largest city, Tbilisi. Ethnic Georgians, who are native to the region, constitute a majority of the country's population and are its titular nation. Georgia has been inhabited since prehistory, hosting the world's earliest known sites of winemaking, gold mining, and textiles. The Classical antiquity, classical era saw the emergence of several kingdoms, such as Colchis and Kingdom of Iberia, Iberia, that formed the nucleus of the modern Georgian state. In the early fourth centu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tashkent
Tashkent (), also known as Toshkent, is the Capital city, capital and List of cities in Uzbekistan, largest city of Uzbekistan. It is the most populous city in Central Asia, with a population of more than 3 million people as of April 1, 2024. It is located in northeastern Uzbekistan, near the border with Kazakhstan. Before the influence of Islam in the mid-8th century AD, Sogdian people, Sogdian and Turkic people, Turkic culture was predominant. After Genghis Khan destroyed the city in 1219, it was rebuilt and profited from its location on the Silk Road. From the 18th to the 19th centuries, the city became an Tashkent (1784), independent city-state, before being re-conquered by the Khanate of Kokand. In 1865, Tashkent fell to the Russian Empire; as a result, it became the capital of Russian Turkestan. In Soviet Union, Soviet times, it witnessed major growth and demographic changes due to Population transfer in the Soviet Union, forced deportations from throughout the Soviet Unio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Scholar
Google Scholar is a freely accessible web search engine that indexes the full text or metadata of Academic publishing, scholarly literature across an array of publishing formats and disciplines. Released in Beta release, beta in November 2004, the Google Scholar index includes peer-reviewed online academic journals and books, conference papers, theses and dissertations, preprints, Abstract (summary), abstracts, technical reports, and other scholarly literature, including Legal opinion, court opinions and patents. Google Scholar uses a web crawler, or web robot, to identify files for inclusion in the search results. For content to be indexed in Google Scholar, it must meet certain specified criteria. An earlier statistical estimate published in PLOS One using a mark and recapture method estimated approximately 79–90% coverage of all articles published in English with an estimate of 100 million.'' Trend Watch'' (2014) Nature (journal), Nature 509(7501), 405 – discussing Madian K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1936 Births
Events January–February * January 20 – The Prince of Wales succeeds to the throne of the United Kingdom as King Edward VIII, following the death of his father, George V, at Sandringham House. * January 28 – Death and state funeral of George V, State funeral of George V of the United Kingdom. After a procession through London, he is buried at St George's Chapel, Windsor Castle. * February 4 – Radium E (bismuth-210) becomes the first radioactive element to be made synthetically. * February 6 – The 1936 Winter Olympics, IV Olympic Winter Games open in Garmisch-Partenkirchen, Germany. * February 10–February 19, 19 – Second Italo-Ethiopian War: Battle of Amba Aradam – Italian forces gain a decisive tactical victory, effectively neutralizing the army of the Ethiopian Empire. * February 16 – 1936 Spanish general election: The left-wing Popular Front (Spain), Popular Front coalition takes a majority. * February 26 – February 26 Incident (二・二六事件, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Mathematicians From Georgia (country)
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men (Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudican revolt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
