Semiparametric model
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\}](/Images/godic/202502/10/b2451c7691da7d396fd748a4771258933043.png")
indexed by a parameter ![\theta](/Images/godic/202502/10/50d91f80cbb8feda1d10e167107ad1ff3043.png")
.
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.