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