Show that the pure shrinkage estimator (Problem 9.25) is the solution to

Data From Problem 9.25

The pure shrinkage estimator is defined as \(\hat{\beta}_{s}=c \hat{\beta}\), were \(0 \leq c \leq 1\) is a constant chosen by the analyst. Describe the kind of shrinkage that this estimator introduces, and compare it with the shrinkage that results from ridge regression. Intuitively, which estimator seems preferable?

\[
\begin{gathered}
\underset{\beta}{\operatorname{Minimize}}(\beta-\hat{\beta})^{\prime}(\beta-\hat{\beta}) \\
\text { subject to } \beta^{\prime} \beta \leq d^{2}
\end{gathered}
\]