= Solution
An <admissible estimator> is one for which there is no estimator $\delta$ satisfying
$$
R(\theta,\delta)\leq R(\theta,\widehat\theta)
$$
for every $\theta$, with strict inequality for at least one $\theta$. For $p\geq3$, the <James–Stein estimator>
$$
\delta_{\rm JS}(X)=
\left(1-\frac{p-2}{\lVert X\rVert^2}\right)X
$$
has risk
$$
R(\theta,\delta_{\rm JS})
=p-(p-2)^2\mathbb E_\theta
\frac1{\lVert X\rVert^2}<p.
$$
It strictly dominates $X$, and hence
$$
\boxed{\widehat\theta_{\rm MLE}\text{ is inadmissible}.}
$$
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