|
Hannan–Quinn Information Criterion
In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection. It is an alternative to Akaike information criterion (AIC) and Bayesian information criterion (BIC). It is given as : \mathrm = -2 L_ + 2 k \ln(\ln(n)), \ where ''L_'' is the log-likelihood, ''k'' is the number of parameters, and ''n'' is the number of observations. Burnham & Anderson (2002, p. 287) say that HQC, "while often cited, seems to have seen little use in practice". They also note that HQC, like BIC, but unlike AIC, is not an estimator of Kullback–Leibler divergence. Claeskens & Hjort (2008, ch. 4) note that HQC, like BIC, but unlike AIC, is not asymptotically efficient; however, it misses the optimal estimation rate by a very small \ln(\ln(n)) factor. They further point out that whatever method is being used for fine-tuning the criterion will be more important in practice than the term \ln(\ln(n)), since this latter number is small even for very large n; h ... [...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] |
Focused Information Criterion
In statistics, the focused information criterion (FIC) is a method for selecting the most appropriate model among a set of competitors for a given data set. Unlike most other model selection strategies, like the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the deviance information criterion (DIC), the FIC does not attempt to assess the overall fit of candidate models but focuses attention directly on the parameter of primary interest with the statistical analysis, say \mu , for which competing models lead to different estimates, say \hat\mu_j for model j . The FIC method consists in first developing an exact or approximate expression for the precision or quality of each estimator, say r_j for \hat\mu_j , and then use data to estimate these precision measures, say \hat r_j . In the end the model with best estimated precision is selected. The FIC methodology was developed by Gerda Claeskens and Nils Lid Hjort, first in two 2003 discussion ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The Royal Statistical Society
The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Wiley for the Royal Statistical Society. History The Statistical Society of London was founded in 1834, but would not begin producing a journal for four years. From 1834 to 1837, members of the society would read the results of their studies to the other members, and some details were recorded in the proceedings. The first study reported to the society in 1834 was a simple survey of the occupations of people in Manchester, England. Conducted by going door-to-door and inquiring, the study revealed that the most common profession was mill-hands, followed closely by weavers. When founded, the membership of the Statistical Society of London overlapped almost completely with the statistical section of the British Association for the Advancement of Science. In 1837 a volume of ''Transactions of the Statistical Society of London'' were wri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barry Gerard Quinn
Barry may refer to: People and fictional characters * Barry (name), including lists of people with the given name, nickname or surname, as well as fictional characters with the given name * Dancing Barry, stage name of Barry Richards (born c. 1950), former dancer at National Basketball Association games Places Canada *Barry Lake, Quebec *Barry Islands, Nunavut United Kingdom * Barry, Angus, Scotland, a village ** Barry Mill, a watermill * Barry, Vale of Glamorgan, Wales, a town ** Barry Island, a seaside resort ** Barry Railway Company ** Barry railway station United States * Barry, Illinois, a city * Barry, Minnesota, a city * Barry, Texas, a city * Barry County, Michigan * Barry County, Missouri * Barry Township (other), in several states * Fort Barry, Marin County, California, a former US Army installation Elsewhere * Barry Island (Debenham Islands), Antarctica * Barry, New South Wales, Australia, a village * Barry, Hautes-Pyrénées, France, a commune Arts an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward J
Edward is an English given name. It is derived from the Anglo-Saxon name ''Ēadweard'', composed of the elements '' ēad'' "wealth, fortune; prosperous" and '' weard'' "guardian, protector”. History The name Edward was very popular in Anglo-Saxon England, but the rule of the Norman and Plantagenet dynasties had effectively ended its use amongst the upper classes. The popularity of the name was revived when Henry III named his firstborn son, the future Edward I, as part of his efforts to promote a cult around Edward the Confessor, for whom Henry had a deep admiration. Variant forms The name has been adopted in the Iberian peninsula since the 15th century, due to Edward, King of Portugal, whose mother was English. The Spanish/Portuguese forms of the name are Eduardo and Duarte. Other variant forms include French Édouard, Italian Edoardo and Odoardo, German, Dutch, Czech and Romanian Eduard and Scandinavian Edvard. Short forms include Ed, Eddy, Eddie, Ted, Teddy and Ned ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nils Lid Hjort
Nils Lid Hjort (born 12 January 1953) is a Norwegian statistician, who has been a professor of mathematical statistics at the University of Oslo since 1991. Hjort's research themes are varied, with particularly noteworthy contributions in the fields of Bayesian probability (Beta processes for use in non- and semi-parametric models, particularly within survival analysis and event history analysis, but also with links to Indian buffet processes in machine learning), density estimation and nonparametric regression (local likelihood methodology), model selection ( focused information criteria and model averaging), confidence distributions, and change detection. He has also worked with spatial statistics, statistics of remote sensing, pattern recognition, etc. An article on frequentist model averaging, with co-author Gerda Claeskens, was selected as ''Fast Breaking Paper in the field of mathematics'' by the Essential Science Indicators in 2005. This and a companion paper, both publis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerda Claeskens
Gerda Claeskens is a Belgian statistician. She is a professor of statistics in the Faculty of Economics and Business at KU Leuven, associated with the KU Research Centre for Operations Research and Business Statistics (ORSTAT). Contributions Claeskens is an expert in nonparametric statistics and in model selection, including model averaging. She is known for developing, with Nils Lid Hjort, the focused information criterion for model selection. With Hjort, she is the author of the book ''Model Selection and Model Averaging'' (Cambridge University Press, 2008). Education and career Claeskens earned a licentiate in mathematics at the University of Antwerp in 1995. In 1999, she earned a master's degree in biostatistics and Ph.D. in mathematics, at Limburgs Universitair Centrum (now the University of Hasselt); her dissertation, supervised by Marc Aerts, was ''Smoothing Techniques and Bootstrap Methods for Multiparameter Likelihood''. She did postdoctoral research at the Australian Na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shibata Information Criterion , Train Coupler
{{disambiguation, geo ...
Shibata may refer to: Places * Shibata, Miyagi, a town in Miyagi Prefecture * Shibata District, Miyagi, a district in Miyagi Prefecture * Shibata, Niigata, a city in Niigata Prefecture ** Shibata Station (Niigata), a railway station in Niigata Prefecture * Shibata Station (Aichi), a railway station in Aichi Prefecture Other uses * Shibata (surname), a Japanese surname *Shibata clan, Japanese clan originating in the 12th century *Shibata coupler A coupling (or a coupler) is a mechanism typically placed at each end of a railway vehicle that connects them together to form a train. A variety of coupler types have been developed over the course of railway history. Key issues in their desig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deviance Information Criterion
The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC). It is particularly useful in Bayesian model selection problems where the posterior distributions of the models have been obtained by Markov chain Monte Carlo (MCMC) simulation. DIC is an asymptotic approximation as the sample size becomes large, like AIC. It is only valid when the posterior distribution is approximately multivariate normal. Definition Define the deviance as D(\theta)=-2 \log(p(y, \theta))+C\, , where y are the data, \theta are the unknown parameters of the model and p(y, \theta) is the likelihood function. C is a constant that cancels out in all calculations that compare different models, and which therefore does not need to be known. There are two calculations in common usage for the effective number of parameters of the model. The first, as described in , is p_D=\overline-D(\bar), where \bar is the expectation of \theta. The second, as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Selection
Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be the best choice (Occam's razor). state, "The majority of the problems in statistical inference can be considered to be problems related to statistical modeling". Relatedly, has said, "How hetranslation from subject-matter problem to statistical model is done is often the most critical part of an analysis". Model selection may also refer to the problem of selecting a few representative models from a large set of computational models for the purpose of decision making or optimization under uncertainty. Introduction In its most basic forms, model selection is one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of The Iterated Logarithm
In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Ya. Khinchin (1924). Another statement was given by A. N. Kolmogorov in 1929. Statement Let be independent, identically distributed random variables with means zero and unit variances. Let ''S''''n'' = ''Y''1 + ... + ''Y''''n''. Then : \limsup_ \frac = 1 \quad \text, where “log” is the natural logarithm, “lim sup” denotes the limit superior, and “a.s.” stands for “almost surely”. Discussion The law of iterated logarithms operates “in between” the law of large numbers and the central limit theorem. There are two versions of the law of large numbers — the weak and the strong — and they both state that the sums ''S''''n'', scaled by ''n''−1, converge to zero, respectively in probability and almost surely: : \frac \ \xrightarrow\ 0, \qquad \frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Efficiency (statistics)
In statistics, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator, needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound. An ''efficient estimator'' is characterized by having the smallest possible variance, indicating that there is a small deviance between the estimated value and the "true" value in the L2 norm sense. The relative efficiency of two procedures is the ratio of their efficiencies, although often this concept is used where the comparison is made between a given procedure and a notional "best possible" procedure. The efficiencies and the relative efficiency of two procedures theoretically depend on the sample size available for the given procedure, but it is often possible to use the asymptotic relative efficiency (defined as the limit of the relative efficiencies as the sample size grows) as the principal compariso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
