Nonparametric empirical Bayes estimator in simultaneous estimation of Poisson means with application to mass spectrometry data

We consider the problem of simultaneous Poisson mean vector estimation and discuss the performance of nonparametric empirical Bayes (NPEB) estimator from the view point of risk consistency. We define the structural uniform risk consistency with respect to some classes of priors and show that the NPEB estimator achieves a structural uniform risk consistency with respect to some class of priors. It is shown that the NPEB estimator performs better than the maximum-likelihood estimator (MLE) and James–Stein estimators from the view point of structural uniform risk consistency. We also present numerical studies which support the asymptotic results and compare with the MLE and James–Stein-type estimators. We provide a real example of mass spectrometry data from a breast cancer study in Sauter et al. [Sauter, E.R., Davis, W., Qin, W., Scanlon, S., Mooney, B., Bromert, K., and Folk, W.R. (2009), ‘Identification of a β-Casein-Like Peptide in Breast Nipple Aspirate Fluid that is Associated with Breast Cancer’, Biomarkers in Medicine, 3, 577–588] with comparison of various estimators.