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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 arti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "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. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiparametric Model
In statistics, a semiparametric model is a statistical model that has parametric and nonparametric components. A statistical model is a parameterized family of distributions: \ indexed by a parameter \theta. * A parametric model is a model in which the indexing parameter \theta is a vector in k-dimensional Euclidean space, for some nonnegative integer k.. Thus, \theta is finite-dimensional, and \Theta \subseteq \mathbb^k. * With a nonparametric model, the set of possible values of the parameter \theta is a subset of some space V, which is not necessarily finite-dimensional. For example, we might consider the set of all distributions with mean 0. Such spaces are vector spaces with topological structure, but may not be finite-dimensional as vector spaces. Thus, \Theta \subseteq V for some possibly infinite-dimensional space V. * With a semiparametric model, the parameter has both a finite-dimensional component and an infinite-dimensional component (often a real-valued funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shibata Information Criterion
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) Shibata (written: lit. "brushwood, ricefield") is the 63rd most common Japanese surname. Less common variants are and . Notable people with the surname include: *, Japanese swimmer *, Japanese field hockey player *, Japanese volleyball player *, ..., a Japanese surname * Shibata clan, Japanese clan originating in the 12th century * Shibata coupler, Train Coupler {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. According to Burnham and Anderson, HQIC, "while often cited, seems to have seen little use in practice" (p. 287). They also note that HQIC, like BIC, but unlike AIC, is not an estimator of Kullback–Leibler divergence. Claeskens and Hjort 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 (ch. 4). 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] |
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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Hazards Models
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. The hazard rate at time t is the probability per short time d''t'' that an event will occur between t and t + dt given that up to time t no event has occurred yet. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed, may double its hazard rate for failure. Other types of survival models such as accelerated failure time models do not exhibit proportional hazards. The accelerated failure time model describes a situation where the biological or mechanical life history of an event is accelerated (or decelerated). Background ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Linear Model
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation (MLE) of the model parameters. MLE remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian regression and least squares fitting to variance stabilized responses, have been developed. Intuition Ordinary linear regression predicts the expected value of a given unknown quanti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariate
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, on the other hand, are not seen as depending on any other variable in the scope of the experiment in question. Rather, they are controlled by the experimenter. In pure mathematics In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers)Carlson, Robert. A concrete introduction to real analysis. CRC Press, 2006. p.183 and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is , and the most common symbol for the output is ; the function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Size
Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complex studies, different sample sizes may be allocated, such as in stratified surveys or experimental designs with multiple treatment groups. In a census, data is sought for an entire population, hence the intended sample size is equal to the population. In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group. Sample sizes may be chosen in several ways: *using experience – small samples, though sometimes unavoidable, can result in wid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-parametric Statistics
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated. Definitions The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: The first meaning of ''nonparametric'' involves techniques that do not rely on data belonging to any particular parametric family of probability distributions. These include, among others: * Methods which are ''distribution-free'', which do not rely on assumptions that the data are drawn from a given parametric family of probability distributions. * Statistics defined to be a function on a sample, without dependency on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
