The mean square error criterion for ridge regression is [ Eleft(L_{1}^{2} ight)=sum_{j=1}^{p} frac{lambda_{j}}{left(lambda_{j}+k ight)^{2}}+sum_{j=1}^{p} frac{alpha_{j}^{2} k^{2}}{left(lambda_{j}+k ight)^{2}} ] Try to find the value of (k)

The mean square error criterion for ridge regression is

\[
E\left(L_{1}^{2}\right)=\sum_{j=1}^{p} \frac{\lambda_{j}}{\left(\lambda_{j}+k\right)^{2}}+\sum_{j=1}^{p} \frac{\alpha_{j}^{2} k^{2}}{\left(\lambda_{j}+k\right)^{2}}
\]

Try to find the value of \(k\) that minimizes \(E\left(L_{1}^{2}\right)\). What difficulties are encountered?