Derivative estimation and testing in generalized additive models

Estimation and testing procedures for generalized additive (interaction) model are developed. We present extensions of several existing procedures for additive models when the link is the identity. This set of methods includes estimation of all component functions and their derivatives, testing functional forms and in particular variable selection. Theorems and simulation results are presented for the fundamentally new procedures. These comprise of, in particular, the introduction of local polynomial smoothing for this kind of models and the testing, including variable selection. Our method is straightforward to implement and the simulation studies show good performance in even small data sets

Structural tests in additive regression

We consider the component analysis problem for a regression model with an additive structure. The problem is to test if some of the additive components is of polynomial structure, e.g. linear, without specifying the structure of the remaining components. A particular case is the problem of selecting the significant covariates. The presented method is based on the wavelet transform using the Haar basis, which allows for applications under mild conditions on the design and smoothness of the regression function. The results demonstrate that each component of the model can be tested with the rate corresponding to the case if all the remaining components were known. The proposed procedure is also computationally straightforward. Simulation results and a real data example about female labor supply demonstrate the good performance of the test

Bootstrap inference in semiparametric generalized additive models

Semiparametric generalized additive models are a powerful tool in quantitative econometrics. The main focus is the application of bootstrap methods. It is shown that bootstrap can be used for bias correction, hypothesis testing (e.g. component-wise analysis) and the construction of uniform confidence bands. Various bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of our methods is illustrated in simulations and in an application to East-West German migration

Anthropogenic organic micro-pollutants and pathogens in the urban water cycle: assessment, barriers and risk communication (ASKURIS)

In urban areas, water often flows along a partially closed water cycle in which treated municipal wastewater is discharged into surface waters which are one source of raw waters used for drinking water supply. A number of organic micro-pollutants (OMP) can be found in different water compartments. In the near future, climatic and demographic changes will probably contribute to an increase of OMP and antibiotic-resistant pathogens in aquatic ecosystems. The occurrence of OMP, possible adverse effects on aquatic organisms and human health and the public perception must be carefully assessed to properly manage and communicate potentially associated risks and to implement appropriate advanced treatment options at the optimum location within the water cycle. Therefore, the interdisciplinary research project ASKURIS focuses on identification and quantification, toxicological assessment and removal of organic micro-pollutants and antibiotic-resistant pathogens in the Berlin water cycle, life cycle-based economic and environmental assessment, public perception and management of potential risks