Abstract

We consider the statistical problem of estimating constituent curves from aggregated curves, called aggregated functional data, in models with additive gaussian and positive random errors. This problem occurs in several areas of science, such as chemometrics, when absorbance curves of constituents of a given substance need to be estimated from samples of its aggregated absorbance curve, according to the Beer-Lambert Law. We propose the use of wavelets representation of the constituent curves and the application of suitable Bayesian shrinkage rules to estimate the coefficients of the representations. This procedure has the advantages of estimating curves with important local features, such as discontinuities, peaks and oscillations and representing the estimated curves in a sparse way by a few number of nonzero coefficients. We studied the statistical properties of the estimators and evaluated the performance of the proposed method in several Monte Carlo simulations. In addition, applications on real datasets were also done.