Linear estimator in nonparametric regression

A linear estimator at $x_0$ has the form $\hat{m}(x_0)={\sum }_i{W}_i(x_0)Y_i$, where the weights depend on the design and tuning parameters but not on the observed responses.

A smoothing matrix maps an observation vector linearly to fitted values, $\hat{Y}=SY$. Its diagonal entries quantify each observation's direct contribution to its own fitted value.