semiparametrisissä

Semiparametric models represent a blend of parametric and nonparametric statistical approaches. In a parametric model, the functional form of the relationship between variables is fully specified, for example, a linear regression model where the relationship is assumed to be of the form y = β₀ + β₁x + ε. In contrast, a nonparametric model makes very few assumptions about the functional form, allowing the data to dictate the shape of the relationship, such as in kernel regression.

Semiparametric models strike a balance by specifying some parts of the model parametrically and leaving other parts unspecified or nonparametric. This allows for flexibility where little is known about the relationship and precision where a parametric form is justifiable. A common example is a semiparametric regression model, which might specify the relationship for some covariates parametrically while modeling the effect of other covariates nonparametrically. This is often beneficial when there is prior knowledge or theoretical justification for a parametric form for certain variables, but uncertainty regarding others.

The appeal of semiparametric models lies in their ability to achieve the efficiency of parametric models when their assumptions are correct, while retaining the robustness and flexibility of nonparametric models when those assumptions are violated. This makes them useful in a wide range of applications, including survival analysis, econometrics, and machine learning, where capturing complex data structures while maintaining some interpretability is desired. The estimation of semiparametric models often involves more complex algorithms than purely parametric or nonparametric methods, but offers a powerful compromise.