Parametric Model
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In statistics, a parametric model or parametric family or finite-dimensional model is a family of probability distribution|distributions that can be described using a finite number of parameters. These parameters are usually collected together to form a single k-dimensional parameter vector θ = (θ1, θ2, …, θ'k).Parametric models are contrasted with the semiparametric model|semi-parametric, semi-nonparametric model|semi-nonparametric, and non-parametric models, all of which consist of an infinite set of “parameters” for description. The distinction between these four classes is as follows: * in a “parametric” model all the parameters are in finite-dimensional parameter spaces; * a model is “nonparametric” if all the parameters are in infinite-dimensional parameter spaces; * a “semi-parametric” model contains finite-dimensional parameters of interest and infinite-dimensional nuisance parameters; * a “semi-nonparametric” model has both finite-dimensional and infinite-dimensional unknown p...
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