The [James-Stein Estimator](http://en.wikipedia.org/wiki/James%E2%80%93Stein_estimator).

Suppose $Y \in \mathbb{R}^n$ is a Gaussian vector with unknown mean $\mu$ and known spherical variance $\sigma^2I$. Given an observation of $Y$, we are interested in finding an estimator $\hat{\mu}$ of $\mu$ which minimizes the expected mean squared risk $R(\hat{\mu}) := E(||\hat{\mu} - \mu||^2)$. 

For $n \le 2$, the Gauss-Markov estimator, $\hat{\mu}_{GM} = Y$ minimizes $R(\hat{\mu})$. But for $n \ge 3$ the James-Stein estimator

$$
\hat{\mu}_{JS} = \left(1 - \frac{(n-2)\sigma^2}{||Y||^2}\right)Y
$$

satisfies $R(\hat{\mu}_{JS}) \le R(\hat{\mu}_{GM})$. Note however, that the James-Stein estimator itself does not minimize the mean squared risk.