Gel ' fand n-Widths and the Method of Least Squares

Abstract

Consider the problem of estimating a function f known to lie in a convex, compact subset F of L2[0, 1], when one observes data on f containing white Gaussian noise. We establish an upper bound on the integrated mean-squared error of least-squares estimates which uses the asymptotic properties of the Gel'fand n-widths of F. The bound shows that if the Gel… (More)

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