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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#### Best Answer

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):

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.161.8881&rep=rep1&type=pdf

**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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