These classical methods are based on the assumption of a normal distribution for the random errors. Since this assumption is often unwarranted, robust methods have been developed in the last 30 years. Powerful general results are available for the class of M-estimators. They allow for a straightforward "robustification" of the mentioned classical methods. A number of extensions needs further resarch, which will be undertaken in this project.
Regression models with correlated errors -- as described -- are needed, among many other examples, when studying emissions of road traffic in so-called tunnel studies. Observed concentrations of air pollutants in a road tunnel in short time intervals are described as a function of the numbers of vehicles of different classes and of the traffic speed. Such a study has been conducted in 1993 in the Gubrist tunnel near Zürich and has been analyzed by our group using classical and robust methods. Further tunnel studies are planned by the Atmospheric Chemistry Group of the Labor für Atmosphärenphysik (LAPETH). Their analysis will be part of this project.