Nonparametric deconvolution of density estimation based on observed sums

This paper develops a methodology for distribution-free estimation of a density function based on observed sums or pooled data. The proposed methods employ a Fourier approach to nonparametric deconvolution of a density estimate. Asymptotic normality is established and an upper bound for the integrated absolute error is given for the proposed density estimator. Monte Carlo simulations are used to examine the performance of the density estimators. The proposed techniques are exemplified using data from a study of biomarkers associated with coronary heart disease.