Signal denoising is the process of reducing the unwanted noise in order to restore the original signal. Donoho and Johnstone’s denoising algorithm based on wavelet thresholding replace the small coefficients by zero and keep or shrink the coefficients with absolute value above the threshold. So the threshold selection becomes more important in signal denoising. In this paper the threshold selec...

This work addresses the unification of some basic functions and thresholds used in nonparametric estimation of signals by shrinkage in the wavelet domain. The Soft and Hard thresholding functions are presented as degenerate smooth sigmoid based shrinkage functions. The shrinkage achieved by this new family of sigmoid based functions is then shown to be equivalent to a regularisation of wavelet ...

This paper presents a new signal denoising method based on the classical three step procedure analysis-thresholdsynthesis and the Spectral Intrinsic Decomposition (SID). This method consists of an iterative thresholding of the SID components. If the wavelets denoising approach depends on the choice of the wavelet form, the SID-denoising proposed in this paper is self adaptive. The SID-based rem...

We investigate shrinkage priors for constructing Bayesian predictive distributions. It is shown that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or other vague priors if the model manifold satisfies some differential geometric conditions. Kullback– Leibler divergence from the true distribution to a predic...

High-dimensional and highly correlated data leading to non- or weakly identified effects are commonplace. Maximum likelihood will typically fail in such situations and a variety of shrinkage methods have been proposed. Standard techniques, such as ridge regression or the lasso, shrink estimates toward zero, with some approaches allowing coefficients to be selected out of the model by achieving ...