Extreme value analysis of frame coefficients and applications

Markus Haltmeier (Universität Innsbruck)
Wednesday, January 28, 2015 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Consider the problem of estimating a high-dimensional vector from linear observations that are corrupted by additive Gaussian white noise. Many solution approaches for such problems construct an estimate as the most regular element satisfying a bound on the coefficients of the residuals with respect to some frame. In order that the true parameter is feasible, the coefficients of the noise must satisfy the bound. For that purpose we compute the asymptotic distribution of these coefficients. We show that generically a standard Gumbel law results, as it is known from the case of orthonormal bases. However, for highly redundant frames other limiting laws may occur. We discuss applications of such results for thresholding in redundant wavelet or curvelet frames, and for the Dantzig selector.