In statistics, a semiparametric model is a statistical model that has parametric and nonparametric components. A statistical model is a parameterized family of distributions: 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, 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 kernels.

Example

A well-known example of a semiparametric model is the Cox proportional hazards model. If we are interested in studying the time T to an event such as death due to cancer or failure of a light bulb, the Cox model specifies the following distribution function for T: where x is the covariate vector, and \beta and are unknown parameters. . Here \beta is finite-dimensional and is of interest; is an unknown non-negative function of time (known as the baseline hazard function) and is often a nuisance parameter. The set of possible candidates for is infinite-dimensional.