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Khmaladze Transformation
In statistics, the Khmaladze transformation is a mathematical tool used in constructing convenient goodness of fit tests for hypothetical distribution functions. More precisely, suppose X_1,\ldots, X_n are i.i.d., possibly multi-dimensional, random observations generated from an unknown probability distribution. A classical problem in statistics is to decide how well a given hypothetical distribution function F, or a given hypothetical parametric family of distribution functions \, fits the set of observations. The Khmaladze transformation allows us to construct goodness of fit tests with desirable properties. It is named after Estate V. Khmaladze. Consider the sequence of empirical distribution functions F_n based on a sequence of i.i.d random variables, X_1,\ldots, X_n, as ''n'' increases. Suppose F is the hypothetical distribution function of each X_i. To test whether the choice of F is correct or not, statisticians use the normalized difference, : v_n(x)=\sqrt _n(x)-F( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Distribution
In statistical hypothesis testing, the null distribution is the probability distribution of the test statistic when the null hypothesis is true. For example, in an F-test, the null distribution is an F-distribution. Null distribution is a tool scientists often use when conducting experiments. The null distribution is the distribution of two sets of data under a null hypothesis. If the results of the two sets of data are not outside the parameters of the expected results, then the null hypothesis is said to be true. Examples of application The null hypothesis is often a part of an experiment. The null hypothesis tries to show that among two sets of data, there is no statistical difference between the results of doing one thing as opposed to doing a different thing. For an example of this, a scientist might be trying to prove that people who walk two miles a day have healthier hearts than people who walk less than two miles a day. The scientist would use the null hypothesis to test ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empirical Process
In probability theory, an empirical process is a stochastic process that describes the proportion of objects in a system in a given state. For a process in a discrete state space a population continuous time Markov chain or Markov population model is a process which counts the number of objects in a given state (without rescaling). In mean field theory, limit theorems (as the number of objects becomes large) are considered and generalise the central limit theorem for empirical measures. Applications of the theory of empirical processes arise in non-parametric statistics. Definition For ''X''1, ''X''2, ... ''X''''n'' independent and identically-distributed random variables in R with common cumulative distribution function ''F''(''x''), the empirical distribution function is defined by :F_n(x)=\frac\sum_^n I_(X_i), where I''C'' is the indicator function of the set ''C''. For every (fixed) ''x'', ''F''''n''(''x'') is a sequence of random variables which converge to ''F''(''x'') almost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hira L
Hira may refer to: Places *Cave of Hira, a cave associated with Muhammad *Al-Hirah, an ancient Arab city in Iraq ** Battle of Hira, 633AD, between the Sassanians and the Rashidun Caliphate * Hira Mountains, Japan *Hira, New Zealand, settlement north-east of Nelson, New Zealand *Hira (ghetto), an old Jewish ghetto in Tunis, see History of the Jews in Tunisia *Hira (Greece), an ancient Greek settlement Other uses *Hira (surname) *Hira (given name) *Hira (mythical monster), among the Songhai people of West Africa *The Hira Company Ltd, the parent company of Texet Sales Ltd, a British distributor of calculators and electronic devices * HIRA, a gene * Hazard Identification and Risk Assessment, a technique used to identify add address occupational safety and health risks *"Hira", a song by Redgum from their 1984 album ''Frontline'' *Health Insurance Review and Assessment Service (HIRA), a government agency in South Korea *, the ISO 15924 script code for Hiragana See also * Heera (d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jushan Bai
Jushan Bai () is a Chinese American economist. He is a professor of economics at Columbia University. Biography Bai received his B.A. from Nankai University in 1985, M.A. from Pennsylvania State University in 1988, and Ph.D. from University of California, Berkeley in 1992. He taught at Massachusetts Institute of Technology, Boston College, and New York University before joining the Columbia faculty in 2008. Bai specializes in econometrics and is hailed as one of the most prominent economists of Chinese descent by the Chinese press. He was elected a fellow of the Econometric Society The Econometric Society is an international society of academic economists interested in applying statistical tools to their field. It is an independent organization with no connections to societies of professional mathematicians or statisticians. ... in 2013. References {{DEFAULTSORT:Bai, Jushan Living people Chinese economists American economists Nankai University alumni Pennsylvania S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winfried Stute
Winfried is a masculine German given name. Notable people with the name include: *Winfried Berkemeier (born 1953), former German footballer *Winfried Bischoff (born 1941), German-British businessperson *Winfried Bönig (born 1959), German organist *Winfried Brugger (born 1950), German academic *Winfried Denk (born 1957), German physicist and neurobiologist *Winfried Glatzeder (born 1945), German television actor *Winfried Hassemer (1940–2014), German criminal law scientist *Winfried Klepsch (born 1956), retired West German long jumper *Winfried Kretschmann (born 1948), German politician *Winfried Michel (born 1948), German recorder player, composer, and editor of music *Winfried Nachtwei (born 1946), German politician *W.G. Sebald (born 1944), German writer and academic (full name Winfried Georg Sebald) *Winfried Otto Schumann (1888–1974), German physicist *Winfried Schäfer (born 1950), German football manager and former player *Winfried Zillig (1905–1963), German composer, m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger Koenker
Roger William Koenker (born February 21, 1947) is an American econometrician mostly known for his contributions to quantile regression. He is currently a Honorary Professor of Economics at University College London. Education and career He finished his degree at Grinnell College in 1969 and obtained his Ph.D. in Economics from the University of Michigan in 1974. In the same year, he was employed as an assistant professor at UIUC. By 1976, he left the university to work as part of the technical staff at Bell Telephone Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mul .... He came back to UIUC in 1983 to teach as a William B. McKinley Professor of Economics and Statistics before becoming a Honorary Professor of Economics at UCL in 2018. Works Koenker is best known for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Statistics
The ''Annals of Statistics'' is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics. It was started in 1973 as a continuation in part of the '' Annals of Mathematical Statistics (1930)'', which was split into the ''Annals of Statistics'' and the ''Annals of Probability''. The journal CiteScore is 5.8, and its SCImago Journal Rank is 5.877, both from 2020. Articles older than 3 years are available on JSTOR, and all articles since 2004 are freely available on the arXiv. Editorial board The following persons have been editors of the journal: * Ingram Olkin (1972–1973) * I. Richard Savage (1974–1976) * Rupert Miller (1977–1979) * David V. Hinkley (1980–1982) * Michael D. Perlman (1983–1985) * Willem van Zwet (1986–1988) * Arthur Cohen (1988–1991) * Michael Woodroofe (1992–1994) * Larry Brown and John Rice (1995–1997) * Hans-Rudolf Künsch and James O. Berger (1998–2000) * John Marden and Jon A. Wellner (2001–2003) * M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Family
In mathematics and its applications, a parametric family or a parameterized family is a indexed family, family of objects (a set of related objects) whose differences depend only on the chosen values for a set of parameters. Common examples are parametrized (families of) Function (mathematics), functions, probability distributions, curves, shapes, etc. In probability and its applications For example, the probability density function of a random variable may depend on a parameter . In that case, the function may be denoted f_X( \cdot \, ; \theta) to indicate the dependence on the parameter . is not a formal argument of the function as it is considered to be fixed. However, each different value of the parameter gives a different probability density function. Then the ''parametric family'' of densities is the set of functions \ , where denotes the parameter space, the set of all possible values that the parameter can take. As an example, the normal distribution is a family ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematical Statistics
The ''Annals of Mathematical Statistics'' was a peer-reviewed statistics journal published by the Institute of Mathematical Statistics from 1930 to 1972. It was superseded by the ''Annals of Statistics'' and the ''Annals of Probability''. In 1938, Samuel Wilks became editor-in-chief of the ''Annals'' and recruited a remarkable editorial staff: Fisher, Neyman, Cramér, Hotelling, Egon Pearson, Georges Darmois, Allen T. Craig, Deming, von Mises Mises or von Mises may refer to: * Ludwig von Mises, an Austrian-American economist of the Austrian School, older brother of Richard von Mises ** Mises Institute, or the Ludwig von Mises Institute for Austrian Economics, named after Ludwig von ..., H. L. Rietz, and Shewhart. References {{reflist External links Annals of Mathematical Statistics at Project Euclid Statistics journals Probability journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goodness Of Fit
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares. Fit of distributions In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: * Bayesian information criterion *Kolmogorov–Smirnov test *Cramér–von Mises criterion *Anderson–Darling test * Shapiro–Wilk test *Chi-squared test *Akaike informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Distribution (continuous)
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, ''a'' and ''b'', which are the minimum and maximum values. The interval can either be closed (e.g. , b or open (e.g. (a, b)). Therefore, the distribution is often abbreviated ''U'' (''a'', ''b''), where U stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable ''X'' under no constraint other than that it is contained in the distribution's support. Definitions Probability density function The probability density function of the continuous uniform distribution is: : f(x)=\begin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
