Nonparametric and Semiparametric Modelling for Data Analysis

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For many scientific problems, nonparametric and semiparametric statistical modelling can contribute to a better understanding and analysis. This includes the application of curve estimation techniques. The P.I. explores models which combine smooth (nonparametric), non-smooth (discontinuous) and parametric components. For high-dimensional data, such as curve data and longitudinal data, a sensible modelling approach includes components which achieve a dimension reduction. These are typically parametric parts of a model, and nonparametric smoothers are then applied in a second step to the dimension reduced data. The P.I. develops models which are geared towards scientific problems which yield data in the form of samples of curves, high dimensional data or discontinuous data. The techniques used include generalized linear models, estimating equations, change-point analysis, random effects modelling and smoothing (in particular, kernel and local polynomial smoothers).The proposed models with discontinuous parts are used to address the question whether the growth of children proceeds continuously or discontinuously. A second application is the modelling of DNA sequences here discontinuities in base frequencies enable DNA segmentation techniques. Further applications include edge detection in image analysis and the segmentation of continuously recorded financial data such as stock market indices. In addition, the P.I. constructs models for the efficient analysis of high dimensional data. An example is dose-response analysis in nutrition with the aim of finding optimal vitamin sources. The P.I. also proposes models for data where an entire function is recorded per experimental unit. Such data occur in many fields, notably the life sciences, and require innovative statistical approaches. A pertinent example are data on the individually recorded egg-laying behavior for a large cohort of medflies. A major question in aging research is the relation between reproduction and longevity. It is therefore of particular interest to apply the proposed models to explore this connection.