Risk bounds for Empirical Bayes estimates of sparse sequences, with applications to wavelet smoothing

by Iain M. Johnstone and Bernard W. Silverman



Software to implement the methods of the papers is written in the S-PLUS language. Mostly the software will also work in R but it hasn’t been fully tested. The routines for single sequences use the standard parts of the language. Those for wavelet transforms make use of the S+Wavelets module.

The main work of the simulations is carried out using the authors' EbayesThresh package but some supplementary routines are used.

sim1.r results of simulation1()

sim1a.r results of simulation1a()

sim2.r results of simulation2()

sim2dec.r results of simulation2(nondecimated=F)

sim3.r results of simulation3()

sim4.r results of fdrsimulation()

sim4dec.r results of fdrsimulation(nondecimated=F)

The NMR data and results as a table, some plots of the data, and some S-PLUS commands used to carry out their analysis.

The unpublished 1998 manuscript Empirical Bayes approaches to mixture problems and wavelet regression by Iain M. Johnstone and Bernard W. Silverman contains some early work of the authors on this topic but has been almost completely superseded by the current work. An Splus implementation of the methods described is available here. The programs use the WaveThresh package.

This page constructed by Bernard Silverman.