Semiparametric model

（重定向自Semiparametric）

In statistics, a semiparametric model is a model that has parametric and nonparametric components.

A model is a collection of distributions: $\{P_\theta: \theta \in \Theta\}$ indexed by a parameter $\theta$ .

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 $\theta$ . 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.

单词	Semiparametric
释义	Semiparametric 英语百科 Semiparametric model （重定向自Semiparametric） In statistics, a semiparametric model is a model that has parametric and nonparametric components. A model is a collection of distributions: $\{P_\theta: \theta \in \Theta\}$ indexed by a parameter $\theta$ . 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 $\theta$ . 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.
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