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- Semiparametric_model abstract "In statistics a semiparametric model is a model that has parametric and nonparametric components.A model is a collection of distributions: indexed by a parameter . A parametric model is one in which the indexing parameter is a finite-dimensional vector (in -dimensional Euclidean space for some integer ); i.e. the set of possible values for is a subset of , or . In this case we say that is finite-dimensional. In nonparametric models, the set of possible values of the parameter is a subset of some space, 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, for some possibly infinite-dimensional space . In semiparametric models, the parameter has both a finite-dimensional component and an infinite-dimensional component (often a real-valued function defined on the real line). Thus the parameter space in a semiparametric model satisfies , where is an infinite-dimensional space.It may appear at first that semiparametric models include nonparametric models, since they have an infinite-dimensional as well as a finite-dimensional component. However, a semiparametric model is considered to be "smaller" than a completely nonparametric model because we are often interested only in the finite-dimensional component of . That is, we are not interested in estimating the infinite-dimensional component. In nonparametric models, by contrast, the primary interest is in estimating the infinite-dimensional parameter. Thus the estimation task is statistically harder in nonparametric models.These models often use smoothing or kernels.".
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- Semiparametric_model subject Category:Semi-parametric_models.
- Semiparametric_model subject Category:Statistical_models.
- Semiparametric_model subject Category:Statistical_theory.
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- Semiparametric_model comment "In statistics a semiparametric model is a model that has parametric and nonparametric components.A model is a collection of distributions: indexed by a parameter . A parametric model is one in which the indexing parameter is a finite-dimensional vector (in -dimensional Euclidean space for some integer ); i.e. the set of possible values for is a subset of , or . In this case we say that is finite-dimensional.".
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