Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607593 | Journal of Approximation Theory | 2012 | 26 Pages |
Abstract
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2L2 norm, and study their approximation properties over Hilbert subspaces of L2L2. The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in a reproducing kernel Hilbert space (RKHS). Our results have implications to the analysis of MM-estimators in models based on finite-dimensional linear approximation of functions, and also to some related packing problems.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Arash A. Amini, Martin J. Wainwright,