Kernel density estimation (${\hat{f}}_{n,h,K}$)

Given independent and identically distributed random variables $X_1,\dots ,X_n$, the kernel density estimate is

For a symmetric bandwidth-$h$ averaging kernel and a density with bounded first derivative, the interior pointwise bias is at most a constant times $h\Vert f^{\prime }{\Vert }_{\infty }$. Near a support boundary, an uncorrected symmetric kernel can instead have nonvanishing bias.