(Georgia Institute of Technology, 1999)
Pensky, Marianna; Vidakovic, Brani
The problem of estimating a density g based on a sample X ₁ X ₂,…,X [subscript n] from p = q ∗ g is considered. Linear and nonlinear wavelet estimators based on Meyer-type wavelets are constructed. The estimators are asymptotically optimal and adaptive if g belongs to the Sobolev space H[superscript α].Moreover, the estimators considered in this paper adjust automatically to the situation when g is supersmooth.
(Georgia Institute of Technology, 1998-03)
Vidakovic, Brani
Wavelet shrinkage, the method proposed by the seminal work of Donoho and Johnstone is a disarmingly simple and efficient way of denoising data. Shrinking wavelet coefficients was proposed from several optimality criteria. In this article a wavelet shrinkage by coherent Bayesian inference in the wavelet domain is proposed. The methods are tested on standard Donoho-Johnstone test functions.