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

A statistical model is a parameterized family indexed by a parameter.

• A parametric model-dimensional Euclidean space..

• With a nonparametric model, which is 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 for some possibly infinite-dimensional space.

• is an infinite-dimensional space.

. That is, the infinite-dimensional component is regarded as a nuisance parameter. 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 kernelss.

Example

A well-known example of a semiparametric model is the Cox proportional hazards model.:

is an unknown non-negative function of time (known as the baseline hazard function) and is often a nuisance parameter is infinite-dimensional.

See also

• Semiparametric regression

• Statistical model

• Generalized method of moments

Notes

References

• Begun, Janet M.; Hall, W. J.; Huang, Wei-Min; Wellner, Jon A. (1983), "Information and asymptotic efficiency in parametric--nonparametric models", Annals of Statistics, 11 (1983), no. 2, 432--452