Nonparametric deconvolution of density estimation based on observed sums

Abstract

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.

Keywords:

• deconvolution
• design of experiments
• Fourier inversion
• nonparametric density estimation
• pooling blood samples

AMS Subject Classification :

• Primary: 62G07
• 62G20
• 62K99
• Secondary: 62P10

Acknowledgements

The authors would like to thank the editor and two referees for suggestions that helped very much to improve this article.