Simulation studies to compare bayesian wavelet shrinkage methods in aggregated functional data

The present work describes simulation studies to compare the performances in terms of averaged mean squared error of bayesian wavelet shrinkage methods in estimating component curves from aggregated functional data. Five bayesian methods available in the literature were considered to be compared in the studies: The shrinkage rule under logistic prior, shrinkage rule under beta prior, large posterior mode (LPM) method, amplitude-scale invariant Bayes estimator (ABE) and Bayesian adaptive multiresolution smoother (BAMS). The so called Donoho-Johnstone test functions, logit and SpaHet functions were considered as component functions and the scenarios were defined according to different values of sample size and signal to noise ratio in the datasets. It was observed that the signal to noise ratio of the data had impact on the performances of the methods. An application of the methodology and the results to the tecator dataset is also done.