Epanechnikov kernel
= Epanechnikov kernel
{c}
{title2=$K_E(u)=\tfrac34(1-u^2)\mathbf1_{\{|u|\leq1\}}$}
The Epanechnikov <kernel for density estimation> is a nonnegative symmetric truncated parabola with integral one, $\mu_2(K_E)=1/5$, and $R(K_E)=3/5$. It has the smallest optimized <asymptotic mean integrated squared error> among nonnegative second-order density kernels, up to rescaling. Its <canonical kernel> has scale $15^{1/5}$ and support $[-15^{1/5},15^{1/5}]$.