# James-Stein shrinkage 'in the wild'?

I am taken by the idea of James-Stein shrinkage (i.e. that a nonlinear function of a single observation of a vector of possibly independent normals can be a better estimator of the means of the random variables, where 'better' is measured by squared error). However, I have never seen it in applied work. Clearly I am not well enough read. Are there any classic examples of where James-Stein has improved estimation in an applied setting? If not, is this kind of shrinkage just an intellectual curiosity?

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James-Stein estimator is not widely used but it has inspired soft thresholding, hard thresholding which is really widely used.

Wavelet shrinkage estimation (see R package wavethresh) is used a lot in signal processing, shrunken centroid (package pamr under R) for classication is used for DNA micro array, there are a lot of examples of practical efficiency of shrinkage...

For theoretical purpose, see the section of candes's review about shrinkage estimation (p20-> James stein and the section after after that one deals with soft and hard thresholding):

EDIT from the comments: why is JS shrinkage less used than Soft/hard Thresh ?

James Stein is more difficult to manipulate (practically and theoretically) and to understand intuitively than hard thresholding but the why question is a good question!

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I guess I'm wondering why the James-Stein estimator isn't widely used. Is it subsumed by these other techniques, or are the conditions of the theorem not met in practice? –  shabbychef Aug 12 '10 at 16:23
according to the paper I quote both James stein and soft/hard thresholding satisfy oracle inequalities. I guess James Stein is more difficult to manipulate og to understand intuitively than hard thresholding but the why question is a good question! –  robin girard Aug 19 '10 at 6:32

Ridge regression is a form of shrinkage. See Draper & Van Nostrand (1979).

Shrinkage has also proved useful in estimating seasonal factors for time series. See Miller and Williams (IJF, 2003).

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+1 for this paper ! my reference for the link between thresholding and penalized estimation was google.fr/… –  robin girard Aug 12 '10 at 8:11