Semiparametrische

Semiparametric, or semiparametrische in Dutch, models blend parametric components that are described by finite-dimensional parameters with nonparametric components that are unspecified functions. The parametric part provides interpretable effects of covariates, while the nonparametric part captures complex or unknown relationships without forcing a rigid form. The overall model is finite-dimensional in beta and infinite-dimensional in the function component.

Common frameworks include the Cox proportional hazards model, which specifies a parametric effect of covariates and leaves the baseline hazard h0(t) unspecified (nonparametric). Another is partially linear models: Y = X'β + f(Z) + error, where β is parametric and f is a smooth function estimated nonparametrically. Generalized additive models are also considered semi-parametric when smooth terms appear alongside parametric terms.

Estimation relies on likelihood-based or estimating equation approaches that separate the parametric and nonparametric parts. Techniques include profile likelihood, backfitting, penalized likelihood with splines or kernels, and sieve methods. Smoothing parameters control the bias-variance trade-off for the nonparametric component. Identifiability constraints (such as centering f) are typically imposed to ensure a unique solution.

Semiparametric methods balance flexibility and interpretability, offering robustness to misspecification of functional form and efficiency for estimating the parametric effects. They are widely used in survival analysis, econometrics, and biostatistics. Drawbacks include higher computational complexity, sensitivity to smoothing choices, and more elaborate asymptotic theory compared with fully parametric models.