What is Shrinkage estimator, James–Stein estimator?

A shrinkage estimator pulls a set of estimates toward a common target. For $X \sim \mathcal N(\theta, \sigma^2I_d)$, the James–Stein estimator toward zero is $\bigl(1 - (d - 2)\sigma^2/\lvert X\rvert^2\bigr)X$; toward the grand mean $\bar X$ it is $\bar X + \bigl(1 - (d - 3)\sigma^2/\sum_i(X_i - \bar X)^2\bigr)(X - \bar X)$, and its positive part truncates the factor at zero.