Random-design nonparametric regression ($Y_i=m(X_i)+{\epsilon }_i,\mathbb{E}[{\epsilon }_i\mid X_i]=0$)

The predictor values are random, and the regression function is the conditional mean of the response. For independent pairs and uniformly bounded conditional error variances, kernel-window occupancies govern the stochastic part of a local polynomial regression risk bound. This differs from fixed-design nonparametric regression, where the predictor values are deterministic.