Local Smoothing Methods for the Analysis of Multivariate Complex Data Structures

Local smoothing methods are a widely used tool in the context of nonparametric regression. The essential idea is to perform a linear or polynomial regression locally in a neighborhood of the target point. This method is generalized in two ways. Firstly, the polynomials are substituted by arbitrary smooth basis functions, and secondly, the estimating methodology, which is based on the least squares method, is modified in a suitable way. It appears that the first concept is useful for bias reduction, while the second one is interesting for robustifcation against outliers in the predictors. As by-products some interesting relations to other mathematical and statistical topics are unveiled, concerning in particular the theorems from Taylor and Horvitz-Thompson. In the further course of the thesis the interest turns to some particular problems which have not been a domain of local methods so far. It turns out that local smoothing methods, suitably combined, are useful for the online monitoring of time series in order to detect sudden breaks or jumps. Finally, the restriction of modelling only functional data is abandoned and a new approach to calculate principal curves, i.e. smooth curves which pass through the ``middle'' of a multidimensional, possibly multiply branched, data cloud, is developed.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Ludwig-Maximilians-Universität

Year

2003

Author dc:creator

• Einbeck, Jochen

Repository record source_url

https://edoc.ub.uni-muenchen.de/1568/

OAI identifier oai:identifier

oai:edoc.ub.uni-muenchen.de:1568