About: Variance function

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In statistics, the variance function is a smooth function which depicts the variance of a random quantity as a function of its mean. The variance function is a measure of heteroscedasticity and plays a large role in many settings of statistical modelling. It is a main ingredient in the generalized linear model framework and a tool used in non-parametric regression, semiparametric regression and functional data analysis. In parametric modeling, variance functions take on a parametric form and explicitly describe the relationship between the variance and the mean of a random quantity. In a non-parametric setting, the variance function is assumed to be a smooth function.

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rdfs:label	Função de variância (pt) Variance function (en) Варіантність (uk)
rdfs:comment	In statistics, the variance function is a smooth function which depicts the variance of a random quantity as a function of its mean. The variance function is a measure of heteroscedasticity and plays a large role in many settings of statistical modelling. It is a main ingredient in the generalized linear model framework and a tool used in non-parametric regression, semiparametric regression and functional data analysis. In parametric modeling, variance functions take on a parametric form and explicitly describe the relationship between the variance and the mean of a random quantity. In a non-parametric setting, the variance function is assumed to be a smooth function. (en) Em Estatística, a função de variância é uma função suave que representa a variância de uma quantidade aleatória como uma função de sua média. A função de variância desempenha um papel importante em muitas configurações de modelagem estatística. É um ingrediente principal no framework do Modelo linear generalizado e uma ferramenta usada em , e . Na modelagem paramétrica, as funções de variância assumem uma forma paramétrica e descrevem explicitamente a relação entre a variância e a média de uma quantidade aleatória. Em um ajuste não-paramétrico, a função de variância é considerada uma função suave. (pt) Варіантність (рос. вариантность, англ. variance, variability, variation; нім. Variation f) — * Варіантність — в мовознавстві: * уявлення про різні способи вираження тієї чи іншої мовної сутності як про її модифікацію, різновиди або як про відхилення від деякої норми; * одна з фундаментальних характеристик одиниць в мовній системі; * У математиці, теорії автоматичного управління — число змінних, які можна змінювати в певних межах. * — в термодинаміці число незалежних інтенсивних змінних, що допускають довільне варіювання без зміни числа та природи фаз термодинамічної системи. (uk)
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dcterms:subject	Actuarial science Nonparametric regression Generalized linear models Nonparametric statistics Functional analysis
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Link from a Wikipage to another Wikipage	Non-parametric regression Bernoulli distribution Variance Actuarial science Mean Gauss–Markov theorem Generalized linear model Semiparametric regression Functional data analysis Gamma distribution Leibniz integral rule Likelihood function Logit Smooth function Statistics Nonparametric regression Least squares Line fitting Alexander Aitken Exponential family Normal distribution Iteratively reweighted least squares Generalized linear models Nonparametric statistics Functional analysis Distance correlation Poisson distribution Generalized linear models Score (statistics) Smoothing Fisher information Heteroscedasticity Quasi-likelihood Overdispersion Random quantity Best linear unbiased estimator Expit
sameAs	Variance function Variance function Variance function Variance function Variance function Variance function
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has abstract	In statistics, the variance function is a smooth function which depicts the variance of a random quantity as a function of its mean. The variance function is a measure of heteroscedasticity and plays a large role in many settings of statistical modelling. It is a main ingredient in the generalized linear model framework and a tool used in non-parametric regression, semiparametric regression and functional data analysis. In parametric modeling, variance functions take on a parametric form and explicitly describe the relationship between the variance and the mean of a random quantity. In a non-parametric setting, the variance function is assumed to be a smooth function. (en) Em Estatística, a função de variância é uma função suave que representa a variância de uma quantidade aleatória como uma função de sua média. A função de variância desempenha um papel importante em muitas configurações de modelagem estatística. É um ingrediente principal no framework do Modelo linear generalizado e uma ferramenta usada em , e . Na modelagem paramétrica, as funções de variância assumem uma forma paramétrica e descrevem explicitamente a relação entre a variância e a média de uma quantidade aleatória. Em um ajuste não-paramétrico, a função de variância é considerada uma função suave. (pt) Варіантність (рос. вариантность, англ. variance, variability, variation; нім. Variation f) — * Варіантність — в мовознавстві: * уявлення про різні способи вираження тієї чи іншої мовної сутності як про її модифікацію, різновиди або як про відхилення від деякої норми; * одна з фундаментальних характеристик одиниць в мовній системі; * У математиці, теорії автоматичного управління — число змінних, які можна змінювати в певних межах. * — в термодинаміці число незалежних інтенсивних змінних, що допускають довільне варіювання без зміни числа та природи фаз термодинамічної системи. (uk)
gold:hypernym	Function
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is Link from a Wikipage to another Wikipage of	Variance functions Generalized functional linear model Generalized linear model Natural exponential family Functional data analysis Functional regression Correlogram Normal distribution Carl Morris (statistician)

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