Robust estimation of mean and variance using environmental data sets with below detection limit observations

Scientists, especially environmental scientists, often encounter trace level concentrations that are typically reported as less than a certain limit of detection, L. Type I left-censored data arises when certain low values lying below L are ignored or unknown as they cannot be measured accurately. In many environmental quality assurance and quality control (QA/QC), and groundwater monitoring applications of the United States Environmental Protection Agency (USEPA), values smaller than L are not required to be reported. However, practitioners still need to obtain reliable estimates of the population mean μ, and the standard deviation (S.D.) σ. The problem gets complex when a small number of high concentrations are observed with a substantial number of concentrations below the detection limit. The high-outlying values contaminate the underlying censored sample, leading to distorted estimates of μ and σ. The USEPA, through the National Exposure Research Laboratory-Las Vegas (NERL-LV), under the Office of Research and Development (ORD), has research interests in developing statistically rigorous robust estimation procedures for contaminated left-censored data sets. Robust estimation procedures based upon a proposed (PROP) influence function are shown to result in reliable estimates of population parameters of mean and S.D. using contaminated left-censored samples. It is also observed that the robust estimates thus obtained with or without the outliers are in close agreement with the corresponding classical estimates after the removal of outliers. Several classical and robust methods for the estimation of μ and σ using left-censored (truncated) data sets with potential outliers have been reviewed and evaluated.