Nonparametric and Robust Statistics

Task, Goals and Contents:

What do you need for a good statistical analysis? A good model of the problem to be analyzed. But how exactly does the model need to be specified? Many statistical methods assume that a statistical model is only known down to a few parameters. The goal is then to use the data to determine the unknown parameters. However, such parametric models often do not properly capture reality and it is difficult to determine when which model is appropriate. Parametric statistical methods are often so specific to the model that they quickly fail completely even when there are small deviations from the model. Nonparametric statistics, on the other hand, do not require a parametric model at all and thus has a much wider applicability. However, it also has disadvantages. Some questions cannot be treated at all or only very awkwardly. Also, the non-parametric methods in parametric models are often much less efficient than the corresponding parametric methods. Robust methods are a compromise. Robust statistical methods are intended for a specific parametric model and have high efficiency for it. In case of deviations from this model, they do not lose their efficiency as much as the parametric methods. Such deviations can be given e.g. by occurring outliers or by misspecification of the model. There are smooth transitions between robust and nonparametric statistics. Both are areas of high dynamism where new methods are constantly being developed. Many of the methods are so computationally intensive that they are only becoming applicable as computing power improves. The working group is therefore intended to be a forum for the presentation and discussion of the many new nonparametric and robust methods.

Topic Selection:

• Nonparametric and robust regression including applications in signal and image processing
• Nonparametric and robust methods of statistical learning such as cluster analysis and classification
• Nonparametric and robust lifetime analysis, application to time series and functional data
• Outlier detection and outlier robust methods
• Data depth
• Robust experimental designs

Chair