|
|
|
|
|
The derivatives of non-parametric methods to analyse data of different experiments make it possible to achieve conlusions with relatively weak mathematical assumptions on the underlying processes. Conniving scale levels, by means of these methods it shall be checked whether or not certain results hold true also in other experiments. In research group C7 mainly three methodical focuses are used for data analysis:
- Resampling techniques (e.g. bootstrap) can be used to extract statistical information under certain preliminaries, e.g.
-- consistency
-- confidence intervals
-- suitable subsamples
-- results about weights and convergence
- Complex analysis of variance in particular of multivariate data is to detect relevant statistical components, which then are to interprete in terms of the respective experiment. Possible methods are
-- principal component analysis
-- independent component analysis
-- kernel based principal component analysis
- Learning methods are suitable to generalise propositions, which are gained by a training process and then
devolved to other experiments. Keywords of the literature are
-- support vector machines
-- kernel regression
-- kernel feature extrction
-- regularized principal manifolds
Non-parametric methods can be interpreted from the statistical point of view. But they may be construed also in the framework of approximation theory. The connection of both approaches yields many advantages. This holds in particular for the statistical learning theory.
The use of kernels permits to maintain linear algorithms while contemporary analysing non-linear phenomenons. The difficulty arises as the quality of the methods depends on a suitable choise of the kernel. Therefore one research task is to construct kernels that are particularly suitable to deal with when considering the problems issuing from synthesis tasks.
|
|
|
|
