Very nice statement from wiki:

When three or more unrelated parameters are measured, their total MSE can be reduced by using a combined estimator such as the James–Stein estimator; whereas when each parameter is estimated separately, the least squares (LS) estimator is admissible.

So I wonder if it offers any new interpretation for distinction between micro(lot of quantum phenomenons) and macro(where everything seems to be defined "more precisely" when "looking at the object as a whole") world.

  • $\begingroup$ Googling for "quantum james-stein estimator", google.com/search?q=quantum+james-stein+estimator, gives an indication that at least some statisticians and physicists have spent time thinking about the applicability of James-Stein estimation to situations in which there are incompatible measurements. My presentiment is that measurement incompatibility is installed into QT at such a low level that it's unlikely that a relatively high level result such as James-Stein will make a fundamental difference. $\endgroup$ – Peter Morgan May 24 '12 at 11:54

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