 Interior first-order bias cancellation for local constant regression

At an interior point where the regression function is differentiable, a symmetric compactly supported regression kernel makes the first-order bias of an estimator vanish asymptotically. In regular fixed-design nonparametric regression with $h\to 0$ and $nh\to \infty$, the local constant estimator then has squared bias of an estimator $o(h^2)$ and variance $R(K)/(nh)+o((nh{)}^{-1})$ for a unit-integral regression kernel. The differentiability remainder is pointwise and need not hold uniformly over a function class.