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Nonparametric regression and local extreme values
Supervisor: Arne Kovac
Theme: Nonparametric Regression
Local extrema play an important role in many problems in science and
engineering, e.g. spectroscopical data typically exhibit several peaks
sticking out of some baseline noise. Numerous methods have been
suggested over the last decades to tackle the problem of removing noise,
but surprisingly most of them are not able to approximate data with the
correct number of local extrema. While some might regularly miss out
certain features from the data, the more common problem is that methods
tend to produce additional artificial local extrema. There are many
applications where local extrema are of high interest and most of them
might form the basis for a PhD project. Spectroscopy is one application
where the correct identification of local extrema is crucial. Although
the general methodology performs already very well, many questions have
risen while working on real data sets. These involve a possible
improvement of the detection of peaks by incorporating knowledge about
their shape, the determination of a baseline and an extension to two-
dimensional spectroscopy methods. Another application are car insurance
data. The problem of calculating fair tariffs in car insurance involves
a spatial component based on the post code of the policy holder. Local
extrema may reflect a different risk structure between people from urban
and rural areas. Estimating the influence of the place of living on the
risk is a possible project and involves extending existing results to
the two-dimensional situation and incorporating many other variables
such as age, gender or the brand of the car.