Content deleted Content added
Line 47:
<li><math>\bold{R}(\operatorname{D}^2 f) = \int (\operatorname{vec} \, \operatorname{D}^2 f (\bold{x})) (\operatorname{vec} \, \operatorname{D}^2 f (\bold{x}))^T \, d\bold{x}</math>
<li>vec is the vector operator which stacks the columns of matrix into a single vector e.g.
<math>\operatorname{vec} \begin{bmatrix} a & c & e\\ b & d & f\end{bmatrix} = \begin{bmatrix} a & b & c & d & e & f\end{bmatrix}^T</math>.
</ul>
This formula of the AMISE is due to <ref name="CD2010"> </ref>
The accuracy of the AMISE approximation is quantified in
<math>\operatorname{MISE} (\bold{H}) = \operatorname{AMISE} (\bold{H}) + o(n^{-1} |\bold{H}|^{-1/2}) + O(\operatorname{tr} \, \bold{H}^2)</math>
| |||