# SCH

## Seminar

### Dimension reduction

Seminar Room 1, Newton Institute

#### Abstract

Ursula Gather joint work with Charlotte Guddat

Progress in computer science in the last decades has practically led to ’floods of data’ which can be stored and has to be handled to gain information of interest therein. As an example, consider data from the field of genetics where the dimension may increase to values up in the thousands. Classical statistical tools are not able to cope with this situation.

Hence, a number of dimension reduction procedures have been developed which may be applied when considering nonparametric regression procedures. The aim is to find a subspace of the predictor space which is of much lower dimension but still contains the important information on the relation between response and predictors.

We will review a number of procedures for dimension reduction (e.g. SIR, SAVE) in multiple regression and consider them under robustness aspects as well. As a special case we include methods for variable selection (e.g. EARTH, SIS) and introduce a new robust approach for the case when n is much smaller than p.

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