Probability

Let \(y = \theta + \sigma \epsilon\) , where \(e \sim \mathcal{N}(0, \sigma^2\mathbf{I})\) is d-dim.

James-Stein estimator gives lower MSE than maximum likelihood estimator (for \(d \geq 3\))

\[ \hat{\theta}_{\text{JS}} = \left(1 - \frac{(d-2)\sigma^2}{\|Y\|^2}\right) Y \]