semiparametria

Semiparametria refers to a class of statistical models that combine elements of both parametric and nonparametric approaches. In these models, some components are specified parametrically, meaning they follow a known distribution or functional form with a finite number of parameters. Other components, however, are treated nonparametrically, allowing for more flexibility and avoiding strong assumptions about their underlying structure. This hybrid approach aims to leverage the efficiency and interpretability of parametric models where appropriate, while also accommodating the complexity and uncertainty often present in real-world data through nonparametric methods.

A common example of semiparametric modeling is the Cox proportional hazards model used in survival analysis. This model assumes that the hazard function is a product of a baseline hazard function, which is left unspecified (nonparametric), and a function of covariates that is specified parametrically. Another example involves generalized linear models where the link function or the variance function is allowed to be nonparametric. The benefit of semiparametric models lies in their ability to provide more robust inferences compared to fully parametric models when the assumed parametric forms are incorrect, and to achieve greater efficiency than fully nonparametric models when the parametric components are correctly specified. Estimation in semiparametric models often involves iterative procedures that estimate the parametric and nonparametric parts simultaneously or sequentially.