Pointwise minimax rate for Hölder density estimation
= Pointwise minimax rate for Hölder density estimation
Over a one-dimensional <Hölder continuity>[Hölder] <probability density function>[density] class of smoothness $\beta$, the optimized pointwise mean-squared error has order $n^{-2\beta/(2\beta+1)}$. A kernel of sufficiently high order balances squared bias $h^{2\beta}$ against <variance> $(nh)^{-1}$.