Smoothing splines have a penalized likelihood motivation (Good and Gaskins 1971) allowing direct application to nonparametric regression in likelihood-based models. The notion of a weighted likelihood for the nonparametric kernel estimation of a regression function is proposed, generalizing the local likelihood theory of Tibshirani and Hastie (1987). Let the data be of the form (xi, Yi) (i= 1, …,n), wherexi∈[0, 1]dare lattice points and theYiare independent random variables from a family of distributions with parameterλi= g(xi), withghaving continuous partial derivatives of orderk≥ 2. The goal is to arrive at a nonparametric estimate λoof λo=g(xo) for a fixed pointxo∈[0, 1]d.We consider the estimator λothat maximizes the weighted likelihood functionW(λ) = Σni=1W[(xo– xi)/b] logf(Yi:λ), withfthe density ofYi, Wa symmetric kernel with compact support, andbthe bandwidth that controls the degree of smoothing. Sufficient conditions for consistency and asymptotic normality of λoare given. If theYiare normal random variables with meanλiand equal variance, then λois the kernel estimator of Priestly—Chao (1972). It is a weighted average ofYicorresponding toxiin a neighborhood ofxo. The kernel governs the weights and the bandwidth controls the size of the neighborhood. The kernel estimator of the relative risk function is developed for censored survival times under the assumption of the Cox proportional hazards model. The weighted likelihood approach based on the full likelihood is illustrated with real and simulated data.