We review a selected class of regularization problems which balance distance to the observations with a penalty on the complexity or size of the solution. Considered are a variety of definitions of 'closeness', and several selected penalties, based on RKHS or l_1 norms.
A class of tuning methods which generalize the GCV to distance criteria other than least squares are noted. Remarks on on model/variable selection methods will be made, including some based on H. Zhang et al, TR 1059r available via the TRLIST at http://www.stat.wisc.edu/~wahba..
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