Propagation functions for monitoring distributional changes

In environmental assessment and monitoring, a primary objective of the investigator is to describe the changes occurring in the environmentally important variables over time. Propagation functions have been proposed to describe the distributional changes occurring in the variable of interest at two different times. McDonald et al. (1992, 1995) proposed an estimator of propagation function under the assumption of normality. We conduct a detailed sensitivity analysis of inference based on the normal model. It turns out that this model is appropriate only for small departures from normality whereas, for moderate to large departures, both estimation and testing of hypothesis break down. Non-parametric estimation of the propagation function based on kernel density estimation is also considered and the robustness of the choice of bandwidth for kernel density estimation is investigated. Bootstrapping is employed to obtain confidence intervals for the propagation function and also to determine the critical regions for testing the significance of distributional changes between two sampling epochs. Also studied briefly is the mathematical form and graphical shape of the propagation function for some parametric bivariate families of distributions. Finally, the proposed estimation techniques are illustrated on a data set of tree ring widths.