Development of a statistical methodology to assess the concentration level of chemical substances in water on the basis of monitoring data : Part IV : confidence intervals for regional parameters estimated from rivers'monitoring data

The Institute of Statistics of UCL has developed during the year 99, in the framework of a contract with Eurochlor, a methodology to summarize the concentration level of chemical substances in the rivers of a region on the basis of monitoring data (Govaerts et al [2001]). The main idea of the approach is to build a statistical distribution to summarize the concentrations observed in the given region and to derive then from it any statistics of interest like a regional mean, percentiles… This methodology is essentially descriptive in the sense that no incertitude measure is attached to the estimators of the regional parameters. This paper, which summarizes the related master thesis of E. Lecoutre [2001], proposes some solutions to derive confidence intervals for regional parameters of interest. Three general methods are investigated : confidence intervals based on the central limit theorem, bootstrap confidence intervals and non-parametric confidence intervals based on ranks. The three methods have been adapted to be able to derive confidence intervals for the region mean and percentiles when they are estimated through one of the possible estimation method : empirical method, and parametric method for complete and for summarized data. The relative qualities of the proposed intervals are compared through a large simulation study and the limitations of the methodology are finally discussed.