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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 Paul Wolfowitz. Life and career Wolfowitz was born in 1910 in Warsaw, Poland, the son of Helen (Pearlman) and Samuel Wolfowitz. He emigrated with his parents to the United States in 1920. In the mid-1930s, Wolfowitz began his career as a high school mathematics teacher and continued teaching until 1942 when he received his Ph.D. degree in mathematics from New York University. While a part-time graduate student, Wolfowitz met Abraham Wald, with whom he collaborated in numerous joint papers in the field of mathematical statistics. This collaboration continued until Wald's death in an airplane crash in 1950. In 1951, Wolfowitz became a professor of mathematics at Cornell University, where he stayed until 1970. From 1970 to 1978 he was at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officially estimated at 1.86 million residents within a greater metropolitan area of 3.1 million residents, which makes Warsaw the 7th most-populous city in the European Union. The city area measures and comprises 18 districts, while the metropolitan area covers . Warsaw is an Alpha global city, a major cultural, political and economic hub, and the country's seat of government. Warsaw traces its origins to a small fishing town in Masovia. The city rose to prominence in the late 16th century, when Sigismund III decided to move the Polish capital and his royal court from Kraków. Warsaw served as the de facto capital of the Polish–Lithuanian Commonwealth until 1795, and subsequently as the seat of Napoleon's Duchy of Warsaw. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dvoretzky–Kiefer–Wolfowitz Inequality
In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz–Massart inequality (DKW inequality) bounds how close an empirically determined distribution function will be to the distribution function from which the empirical samples are drawn. It is named after Aryeh Dvoretzky, Jack Kiefer, and Jacob Wolfowitz, who in 1956 proved the inequality : \Pr\Bigl(\sup_ , F_n(x) - F(x), > \varepsilon \Bigr) \le Ce^\qquad \text\varepsilon>0. with an unspecified multiplicative constant ''C'' in front of the exponent on the right-hand side. In 1990, Pascal Massart proved the inequality with the sharp constant ''C'' = 2, confirming a conjecture due to Birnbaum and McCarty. In 2021, Michael Naaman proved the multivariate version of the DKW inequality and generalized Massart's tightness result to the multivariate case, which results in a sharp constant of twice the number of variables, ''C'' = 2k. The DKW inequality Given a natural nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors are usually experts in their field and teachers of the highest rank. In most systems of List of academic ranks, academic ranks, "professor" as an unqualified title refers only to the most senior academic position, sometimes informally known as "full professor". In some countries and institutions, the word "professor" is also used in titles of lower ranks such as associate professor and assistant professor; this is particularly the case in the United States, where the unqualified word is also used colloquially to refer to associate and assistant professors as well. This usage would be considered incorrect among other academic communities. However, the otherwise unqualified title "Professor" designated with a capital let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Statistics
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Introduction Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling. The initial analysis of the data often follows the study protocol specified prior to the study being conducted. The data from a study can also be analyzed to consider secondary hypotheses inspired by the initial results, or to suggest new studies. A secondary analysis of the data from a planned study uses tools from data analysis, and the process of doing this is mathematical statistics. Data analysis is divided into: * descriptive statistics - the part of st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Wald
Abraham Wald (; hu, Wald Ábrahám, yi, אברהם וואַלד; – ) was a Jewish Hungarian mathematician who contributed to decision theory, geometry, and econometrics and founded the field of statistical sequential analysis. One of his well-known statistical works was written during World War II on how to minimize the damage to bomber aircraft and took into account the survivorship bias in his calculations. He spent his research career at Columbia University. Life and career Wald was born on 31 October 1902 in Kolozsvár, Transylvania, in the Kingdom of Hungary. A religious Jew, he did not attend school on Saturdays, as was then required by the Hungarian school system, and so he was thus homeschooled by his parents until college. His parents were quite knowledgeable and competent as teachers. In 1928, he graduated in mathematics from the King Ferdinand I University. In 1927, he entered graduate school at the University of Vienna, from which he graduated in 1931 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Bank Group
The World Bank Group (WBG) is a family of five international organizations that make leveraged loans to developing countries. It is the largest and best-known development bank in the world and an observer at the United Nations Development Group. The bank is headquartered in Washington, D.C. in the United States. It provided around $98.83 billion in loans and assistance to "developing" and transition countries in the 2021 fiscal year. The bank's stated mission is to achieve the twin goals of ending extreme poverty and building shared prosperity.The World Bank, Press release: "World Bank Group Commitments Rise Sharply in FY14 Amid Organizational Change"July 1 2014, http://www.worldbank.org/en/news/press-release/2014/07/01/world-bank-group-commitments-rise-sharply-in-fy14-amid-organizational-change/ref> Total lending as of 2015 for the last 10 years through Development Policy Financing was approximately $117 billion. Its five organizations are the International Bank for Reconstruc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Deputy Secretary Of Defense
The deputy secretary of defense (acronym: DepSecDef) is a statutory office () and the second-highest-ranking official in the Department of Defense of the United States of America. The deputy secretary is the principal civilian deputy to the secretary of defense, and is appointed by the president, with the advice and consent of the Senate. The deputy secretary, by statute, is designated as the DoD chief management officer and must be a civilian, at least seven years removed from service as a commissioned officer on active-duty at the date of appointment.. The current deputy secretary of defense is Kathleen Hicks, effective February 8, 2021. Hicks is the first woman to serve in this role. History Public Law 81–36, April 2, 1949, originally established this position as the ''under secretary of defense'', however Public Law 81-2 16, August 10, 1949, a.k.a. the 1949 Amendments to the National Security Act of 1947, changed the title to Deputy Secretary of Defense. Former assistan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude E
Claude may refer to: __NOTOC__ People and fictional characters * Claude (given name), a list of people and fictional characters * Claude (surname), a list of people * Claude Lorrain (c. 1600–1682), French landscape painter, draughtsman and etcher traditionally called just "Claude" in English * Madame Claude, French brothel keeper Fernande Grudet (1923–2015) Places * Claude, Texas, a city * Claude, West Virginia, an unincorporated community Other uses * Allied reporting name of the Mitsubishi A5M Japanese carrier-based fighter aircraft * Claude (alligator) Claude is an albino alligator ('' Alligator mississippiensis'') at the California Academy of Sciences. Claude lacks the pigment melanin, resulting in colorless skin, and he has poor eyesight associated with his albinism. Background Claude was ha ..., an albino alligator at the California Academy of Sciences See also * Claude's syndrome, a form of brainstem stroke syndrome {{disambig, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 work as employees or as statistical consultants. Nature of the work According to the United States Bureau of Labor Statistics, as of 2014, 26,970 jobs were classified as ''statistician'' in the United States. Of these people, approximately 30 percent worked for governments (federal, state, or local). As of October 2021, the median pay for statisticians in the United States was $92,270. Additionally, there is a substantial number of people who use statistics and data analysis in their work but have job titles other than ''statistician'', such as actuaries, applied mathematicians, economist An economist is a professional and practitioner in the social science discipline of economics. The individual may also study, develop, and apply ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Jews
American Jews or Jewish Americans are American citizens who are Jewish, whether by religion, ethnicity, culture, or nationality. Today the Jewish community in the United States consists primarily of Ashkenazi Jews, who descend from diaspora Jewish populations of Central and Eastern Europe and comprise about 90–95% of the American Jewish population. During the colonial era, prior to the mass immigration of Ashkenazi Jews, Sephardic Jews who arrived via Portugal represented the bulk of America's then-small Jewish population, and while their descendants are a Minority group, minority today, they, along with an array of other Jewish communities, represent the remainder of American Jews, including other more recent Sephardi Jews, Mizrahi Jews, Beta Israel, Beta Israel-Ethiopian Jews, Jewish ethnic divisions, various other ethnically Jewish communities, as well as a smaller number of Conversion to Judaism, converts to Judaism. The American Jewish community manifests a wide range ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
