Sharp bounds under contaminated or corrupted sampling with verification, with an application to environmental pollutant data

Let F denote a distribution of interest and G a possibly spurious distribution. This article derives and nonparametrically estimates sharp bounds on characteristics of F when the data are a mixture of F and G, and a fraction of the data is verified to be from F. Contaminated and corrupted mixtures, with and without monotonicity restrictions, are analyzed. The methods are particularly useful in analyzing environmental pollutant measurements obtained using gas chromatography-mass spectroscopy. Results are applied to measurements of organic pollutant concentrations from the Love Canal. We argue that a corruption with monotonic verification model may be the most appropriate model for this type of data.