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Abstract: To estimate a possibly multivariate regression function under the general regression setup, , one can use wavelet thresholding as an alternative to conventional nonparametric regression methods. Wavelet thresholding is a simple operation in the wavelet domain that selects a subset of coefficients corresponding to an estimator of when back-transformed. We propose an enhancement to wavelet thresholding by selecting a subset in a semi-supervised fashion in which the neighboring structure and classification function appropriate for wavelet domains are utilized. Wavelet coefficients are classified into two types: labeled, which have either strong or weak magnitudes, and unlabeled, which have in-between magnitudes. Both are connected to neighboring coefficients and belong to a low-dimensional manifold within the set of all wavelet coefficients. The decision to include a coefficient in the model depends not only on its magnitude but also on the labeled and the unlabeled coefficients from its neighborhood. We discuss the theoretical properties of the method and demonstrate its performance in simulated examples. [Copyright &y& Elsevier]

Abstract: This article derives the probability density function (pdf) of the sum of a normal random variable and a (sphered) Student''s -distribution on odd degrees of freedom greater than or equal to three. Apart from its intrinsic interest applications of this result include Bayesian wavelet shrinkage, Bayesian posterior density derivations, calculations in the theoretical analysis of projection indices and computation of certain moments. [Copyright &y& Elsevier]

An usual assumption underlying the use of wavelet shrinkage is that the regression function is assumed to be either periodic or symmetric. However, such an assumption is not always realistic. This paper proposes an effective method for correcting the boundary bias introduced by the inappropriateness of such periodic or symmetric assumption. The idea is to combine wavelet shrinkage with local polynomial regression, where the latter regression technique is known to possess excellent boundary properties. Simulation results from both the univariate and bivariate settings provide strong evidence that the proposed method is extremely effective in terms of correcting boundary bias. [Copyright &y& Elsevier]

In this paper a new wavelet shrinkage technique is proposed and investigated. When data consist of a multiplicity of related noisy signals, we propose a wavelet-based shrinkage estimation procedure to summarize all data components into a single regularized and representative signal (“base-line”). This fusion of information from different runs is done via Stein-type shrinkage rule resulting from an empirical Bayes argument. The proposed shrinkage estimators maximize the predictive density under appropriate model assumptions on the wavelet coefficients. Features of this model-induced shrinkage are that it is “block-vertical” and local in time.The method, called VERTISHRINK, is evaluated on a battery of test signals under various signal-to-noise ratios and various number of vector components. An application in estimating the base-line signal in an experiment in tumor physiology is provided as well. [Copyright &y& Elsevier]