This work characterizes (dyadic homogeneous) wavelet frames for $$L^2({{\mathbb {R}}})$$ by means of spectral techniques. These techniques use decomposability properties the frame operator in representations associated with dilation operator. The approach is closely related to usual Fourier domain fiberization techniques, dual Gramian analysis, and extension principles. Spectral formulas are us...

Abstract Threshold selection plays a key role in various aspects of statistical inference rare events. In this work, two new threshold methods are introduced. The first approach measures the fit exponential approximation above and achieves good performance small samples. second method smoothly estimates asymptotic mean squared error Hill estimator performs consistently well over wide range proc...