Integrated squared density curvature
= Integrated squared density curvature
{title2=$R(f'')=\int(f''(x))^2dx$}
The integrated squared second derivative measures a smooth density's curvature in L2. It supplies the leading integrated squared bias constant of a second-order <kernel density estimator>. For nonzero second moment $\mu_2(K)$, the <asymptotic mean integrated squared error> has bias term $h^4\mu_2(K)^2R(f'')/4$, so greater curvature calls for a smaller <smoothing bandwidth>.