Unit-width box kernel
= Unit-width box kernel
{title2=$K(u)=\mathbf1_{[-1/2,1/2]}(u)$}
The unit-width centred box kernel is $K(u)=\mathbf1_{[-1/2,1/2]}(u)$. It has integral one and squared $L^2$ norm one. Its rescaling $K_h(u)=h^{-1}K(u/h)$ averages a function on intervals of length $h$. It is obtained from the <uniform smoothing kernel> with support $[-1,1]$ by rescaling, and is useful in both <kernel density estimation> and <local polynomial regression>.