Abstract
Overcomplete representations such as wavelets and windowed Fourier expansions have
become mainstays of modern statistical data analysis. Here we derive expressions for the mean
quadratic risk of shrinkage estimators in the context of general finite frames, which include any fullrank
linear expansion of vector data in a finite-dimensional setting. We provide several new results
and practical estimation procedures that take into account the geometric correlation structure of frame
elements. These results motivate aggregation estimators and block thresholding procedures, and
reinforce that the correlations induced by frame structure should be explicitly treated to yield
improvements in estimation. A simulation study confirms these improvements.
Anno
2015
Autori IAC
Tipo pubblicazione
Altri Autori
De Canditiis Daniela