Samples from hazardous waste site investigations frequently come from two or more statistical populations. Assessment of “background” levels of contaminants can be a significant problem. This problem is being investigated at the U.S. Environmental Protection Agency's Environmental Monitoring Systems Laboratory in Las Vegas. This paper describes a statistical approach for assessing background levels from a dataset. The elevated values that may be associated with a plume or contaminated area of the site are separated from lower values that are assumed to represent background levels. It would be desirable to separate the two populations either spatially by Kriging the data or chronologically by a time series analysis, provided an adequate number of samples were properly collected in space and/or time. Unfortunately, quite often the data are too few in number or too improperly designed to support either spatial or time series analysis. Regulations typically call for nothing more than the mean and standard deviation of the background distribution. This paper provides a robust probabilistic approach for gaining this information from poorly collected data that are not suitable for above-mentioned alternative approaches. We assume that the site has some areas unaffected by the industrial activity, and that a subset of the given sample is from this clean part of the site. We can think of this multivariate data set as coming from two or more populations: the background population, and the contaminated populations (with varying degrees of contamination). Using robust M-estimators, we develop a procedure to classify the sample into component populations. We derive robust simultaneous confidence ellipsoids to establish background contamination levels. Some simulated as well as real examples from Superfund site investigations are included to illustrate these procedures. The method presented here is quite general and is suitable for many geological and biological applications.
Key wordsrobust M-estimators influence function background estimation robust confidence limits separation of mixed sample
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- Campbell, N. A., 1984. Mixture Models and Atypical Values: Math. Geol., v. 16, n. 5, p. 465–477.Google Scholar
- Fleischhauer, H., and Korte, N., 1990,Formation of Cleanup Standards for Trace Elements with Probability Plots, Environmental Management (Vol. 14; No. 1): Springer-Verlag, New York, p. 95–105.Google Scholar
- Fowlkes, E. B., 1979, Some Methods for Studying the Mixture of two Normal (Lognormal) Distributions:J. Am. Stat. Assoc., v. 74, n. 367, p. 561–575.Google Scholar
- Holgersson, M., and Jorner, U., 1978. Decomposition of a Mixture into Normal Components. A Review: J. Bio-Med. Comp., v. 9, p. 367–392.Google Scholar
- Sinclair, A. J., 1976,Applications of Probability Graphs in Mineral Exploration, Assoc. of Exploration Geochemists: Rexdale, Ontario, p. 95.Google Scholar
- Singh, A., 1994, Omnibus Robust Procedures for Assessment of Multivariate Normality and Detection of Multivariate Outliers,in G. P. Patil and C. R. Rao, eds.,Multivariate Environmental Statistics: North Holland, Elsevier Science Publishers, p. 445–488.Google Scholar
- Singh, A., and Nocerino, J. 1994, Robust QA/QC for Environmental Applications,in The Proceedings of the Ninth International Conference on Systems Engineering: University of Nevada, Las Vegas, p. 370–374.Google Scholar