Pointwise minimax rate for Lipschitz regression
= Pointwise minimax rate for Lipschitz regression
At an interior target point in regular <fixed-design nonparametric regression>, mean functions with <Lipschitz bound> $L$ have pointwise <minimax risk> of order $(L\sigma^2/n)^{2/3}$ for fixed positive $L,\sigma$ as $n\to\infty$. A <smoothing bandwidth> of order $(\sigma^2/(nL^2))^{1/3}$ balances squared <bias of an estimator> and <variance>; the <two-point lower bound with a triangular bump> gives the matching lower rate.