Abstract: Statistical estimates and procedures that err on the side of caution are often desirable when dealing with public health issues. The U.S. Environmental Protection Agency, under the Superfund program, takes this approach in its determination of human exposure to soil contaminants at toxic waste sites. Due to uncertainties in estimating the true average contaminant concentration based on site sampling and the need to be conservative in assessing health risk, the EPA advocates the use of the 95% upper confidence limit (UCL) on the mean to provide ``reasonable confidence that the true site average will not be underestimated''. Skewness of the underlying distribution of the contaminant contributes to the persistent underestimation of the population mean when sample size is small and the need for a conservative procedure as attempted by the EPA. In this article, we propose an estimator for the mean of positively skewed distributions based on a penalized least squares criterion. When sample size is small or moderate, the new estimator has smaller mean square error and greater probability of falling within two standard deviations of the sample mean above the true mean than the UCL estimator currently being used by EPA.
Key words and phrases: Coverage, penalized least squares, penalty constant, superfund program.