= Mean absolute error bound for local polynomial regression
{title2=$\mathbb E|\widehat m(x)-m(x)|\le C((nh)^{-1/2}+h^s)$}
For equally spaced <fixed-design nonparametric regression>, independent mean-zero uniformly finite-variance errors, a bounded compactly supported kernel, and a uniformly invertible local <Gram matrix>, degree $\ell\ge s-1$ gives the displayed bound for $s$ bounded <derivatives>. Kernel weights have absolute sum $O(1)$ and squared sum $O((nh)^{-1})$. <Polynomial reproduction> removes a degree-$s-1$ <Taylor polynomial>. Without the degree requirement the general <bias of an estimator> is only $O(h^{\min(s,\ell+1)})$.
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