Robust intervals for some environmental applications

Abstract

In an effort to keep the environment clean, local communities, commercial industries, and government agencies, such as the United States Environmental Protection Agency (US EPA), need to assess the extent of contamination at polluted sites. The site characterization results are then used to establish approaches for remediation, to determine background threshold levels of the pollutants of concern, and to make decisions on various environmental monitoring and remediation activities. Some aspects of site characterization depend upon the chemical analyses of soil or water samples collected at the site. In Superfund and other applications these environmental samples are routinely analyzed by the various laboratories participating in quality assurance/quality control (QA/QC) programs, such as the Contract Laboratory Program (CLP) of the US EPA. The performance of those laboratories is typically monitored through statistical quality control (SQC) techniques requiring the use of the estimates of population parameters of location and scale. However, outlying observations, when present, can distort the entire estimation process, which in turn can lead to incorrect decisions. In order to address these issues, several interval estimates have been discussed. The robust procedure based upon the PROP influence function identifies multiple outliers successfully and provides reliable estimates of population parameters. The weights assigned to individual observations are used to obtain estimates of the degrees of freedom (d.f.) associated with the Student's t and other relevant statistics. The appropriate use of these intervals together with the robust estimates of the population parameters and of the associated degrees of freedom result in more accurate and precise statistical regions to be used in these applications.