Semi-parametric model

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

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

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 ${\displaystyle \theta }$. 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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