Comparing wavelets estimators for a set of signals

Abstract

On each object belonging to a certain population, a signal can be observed. We suppose that those signals come from an additive random effect model involving a population pattern, individual effect and intra-individual noise. The main purpose of this paper is to estimate the underlying pattern from a set of signals observed on a random sample of objects of the population at the same time points. If the number of observations per object is a dyadic number, several estimations of the population pattern are proposed using the wavelet transforms. A simulation study is carried out using the four test functions given by Donoho and Johnstone (1994) as patterns, considering two types of individual components and white and correlated noise. The goodness of fit is analysed for the aforementioned four signal types. A threshold obtained by successive iterations, proposed by Baxter and Upton (2002), is also analysed.