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Jack Kiefer (mathematician)
Jack Carl Kiefer (January 25, 1924 – August 10, 1981) was an American mathematical statistician at Cornell University (1952 to 1979) and the University of California, Berkeley (1979 to 1981). His research interests included the optimal design of experiments, which was his major research area, as well as a wide variety of topics in mathematical statistics. Biography Jack Kiefer was born in Cincinnati, Ohio, to Carl Jack Kiefer and Marguerite K. Rosenau. He began his undergraduate studies at the Massachusetts Institute of Technology in 1942, but left after one year, taking up a position as first lieutenant in the United States Air Force during World War II. In 1946, he returned to MIT, graduating with bachelor's and master's degrees in economics and engineering in 1948 under the supervision of Harold Freeman. He then began graduate studies at Columbia University, under the supervision of Abraham Wald and Jacob Wolfowitz, receiving his Ph.D. in mathematical statistics in 1952. W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cincinnati
Cincinnati ( ) is a city in the U.S. state of Ohio and the county seat of Hamilton County. Settled in 1788, the city is located at the northern side of the confluence of the Licking and Ohio rivers, the latter of which marks the state line with Kentucky. The city is the economic and cultural hub of the Cincinnati metropolitan area. With an estimated population of 2,256,884, it is Ohio's largest metropolitan area and the nation's 30th-largest, and with a city population of 309,317, Cincinnati is the third-largest city in Ohio and 64th in the United States. Throughout much of the 19th century, it was among the top 10 U.S. cities by population, surpassed only by New Orleans and the older, established settlements of the United States eastern seaboard, as well as being the sixth-most populous city from 1840 until 1860. As a rivertown crossroads at the junction of the North, South, East, and West, Cincinnati developed with fewer immigrants and less influence from Europe than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow
A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher educational institutions, a fellow can be a member of a highly ranked group of teachers at a particular college or university or a member of the governing body in some universities (such as the Fellows of Harvard College); it can also be a specially selected postgraduate student who has been appointed to a post (called a fellowship) granting a stipend, research facilities and other privileges for a fixed period (usually one year or more) in order to undertake some advanced study or research, often in return for teaching services. In the context of research and development-intensive large companies or corporations, the title "fellow" is sometimes given to a small number of senior scientists and engineers. In the context of medical education in N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hoeffding's Independence Test
In statistics, Hoeffding's test of independence, named after Wassily Hoeffding, is a test based on the population measure of deviation from independence :H = \int (F_-F_1F_2)^2 \, dF_ where F_ is the joint distribution function of two random variables, and F_1 and F_2 are their marginal distribution functions. Hoeffding derived an unbiased estimator of H that can be used to test for independence, and is consistent for any continuous alternative. The test should only be applied to data drawn from a continuous distribution, since H has a defect for discontinuous F_, namely that it is not necessarily zero when F_=F_1F_2. This drawback can be overcome by taking an integration with respect to dF_1F_2. This modified measure is known as Blum–Kiefer–Rosenblatt coefficient. A paper published in 2008Wilding, G.E., Mudholkar, G.S. (2008) "Empirical approximations for Hoeffding's test of bivariate independence using two Weibull extensions", ''Statistical Methodology'', 5 (2), 160-&ndas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Approximation
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive update rules of stochastic approximation methods can be used, among other things, for solving linear systems when the collected data is corrupted by noise, or for approximating extreme values of functions which cannot be computed directly, but only estimated via noisy observations. In a nutshell, stochastic approximation algorithms deal with a function of the form f(\theta) = \operatorname E_ (\theta,\xi) which is the expected value of a function depending on a random variable \xi . The goal is to recover properties of such a function f without evaluating it directly. Instead, stochastic approximation algorithms use random samples of F(\theta,\xi) to efficiently approximate properties of f such as zeros or extrema. Recently, stochastic approximations have found extensive applications in the fields of statistics and machine ... [...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] |
Golden Section Search
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them. If the only extremum on the interval is on a boundary of the interval, it will converge to that boundary point. The method operates by successively narrowing the range of values on the specified interval, which makes it relatively slow, but very robust. The technique derives its name from the fact that the algorithm maintains the function values for four points whose three interval widths are in the ratio ''φ:1:φ'' where ''φ'' is the golden ratio. These ratios are maintained for each iteration and are maximally efficient. Excepting boundary points, when searching for a minimum, the central point is always less than or e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Design
In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with designing experimen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Design Of Experiments
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify control variables that must b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horace White
Horace White (October 7, 1865 – November 27, 1943) was an American lawyer and politician from New York. He was the 37th Governor of New York from October 6, 1910 to December 31, 1910. Life He attended Syracuse Central High School, Cornell University (graduated 1887), and Columbia Law School (graduated 1889), and opened the firm of White, Cheney, Shinaman, and O'Neill in Syracuse, New York in the late 1880s or early 1890s. While at Cornell he was a member of The Kappa Alpha Society. He was a member of the New York State Senate (36th D.) from 1896 to 1907, sitting in the 119th, 120th, 121st, 122nd, 123rd, 124th, 125th, 126th, 127th, 128th, 129th, 130th and 131st New York State Legislatures; and participated in the drawing of the consolidation charter of the City of New York. He was Lieutenant Governor of New York from 1909 to 1910, elected at the New York state election, 1908 on the Republican ticket with Governor Charles Evans Hughes. Hughes resigned in October 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Fisher
Michael Ellis Fisher (3 September 1931 – 26 November 2021) was an English physicist, as well as chemist and mathematician, known for his many seminal contributions to statistical physics, including but not restricted to the theory of phase transitions and critical phenomena. He was the Horace White Professor of Chemistry, Physics, and Mathematics at Cornell University. Later he moved to the University of Maryland College of Computer, Mathematical, and Natural Sciences, where he was University System of Maryland Regents Professor, a Distinguished University Professor and Distinguished Scholar-Teacher. Academic background Michael E. Fisher received his BSc from King's College London in 1951, where he also earned a PhD in physics in 1957, studying analogue computing under Donald MacCrimmon MacKay. He was appointed to the faculty as a lecturer the following year, becoming a full professor in 1965. In 1966 he moved to Cornell University where he became professor of chemistry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute Of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world. Beginning in 2005, the institute started offering joint membership with the Bernoulli Society for Mathematical Statistics and Probability as well as with the International Statistical Institute. The Institute was founded in 1935 with Harry C. Carver and Henry L. Rietz as its two most important supporters. The institute publishes a variety of journals, and holds several international conference every year. Publications The Institute publishes five journals: *''Annals of Statistics'' *'' Annals of Applied Statistics'' *''Annals of Probability'' *''Annals of Applied Probability'' *''Statistical Science'' In addition, it co-sponsors: * The ''Current Index to Statistics'' * '' Electronic Communications in Probability'' * '' El ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
