Wavelet Shrinkage Approaches to Baseline Signal Estimation from Repeated Noisy Measurements

We consider the problem of estimating the baseline signal from repeated noisy measurements taken on some object or individual of interest whose response is not fixed. We devise some wavelet shrinkage schemes to efficiently address the baseline signal estimation problem, adapting some well-known wavelet shrinkage procedures from the standard nonparametric regression literature. These schemes are based on the empirical wavelet coefficients of the observed data. Wavelet decompositions allow one to characterise different types of smoothness conditions assumed on the response function by means of its wavelet coefficients for a wide range of function classes. Furthermore, synthetic data sets, appropriate for baseline signal estimation, are introduced and used to examine the finite sample performance of the various baseline signal estimators. Insight into the performance of the various baseline signal estimators is obtained from numerical tables and graphical outputs. Two real-life data sets, arising from oxygen tension in rats experiments and from human event-related potentials experiments, are also considered as an illustration of the competing baseline signal estimators.