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by mitthrowaway2 775 days ago
Not quite: If the origin is within a standard deviation of |x|² or so (depending on D), then term inside the ReLU is negative, and the adjustment is exactly zero. If the origin is moderately far away from x, then the adjustment is large. If the origin is a vast distance from x, then the adjustment is small in relative terms, but not in absolute terms. The scaling factor approaches zero for large |x| but the displacement between x and û converges toward a constant.

Either way, this is absurd unless we have some additional background information about μ other than our sample x itself. But it's easy to resolve the paradox: Since the choice of origin is arbitrary (unless it isn't!), select our coordinate system such that x = 0, then the adjustment is also zero, and then the James-Stein estimator agrees that û = x = 0.