The fitting of multifunctions: an approach to nonparametric multimodal regression

Einbeck, Jochen; Tutz, Gerhard

The fitting of multifunctions: an approach to nonparametric multimodal regression

Einbeck, Jochen; Tutz, Gerhard

Authors

Professor Jochen Einbeck jochen.einbeck@durham.ac.uk
Professor

Gerhard Tutz

Contributors

A. Rizzi
Editor

M. Vichi
Editor

Abstract

In the last decades a lot of research has been devoted to smoothing in the sense of nonparametric regression. However, this work has nearly exclusively concentrated on fitting regression functions. When the conditional distribution of y|x is multimodal, the assumption of a functional relationship y = m(x) + noise might be too restrictive. We introduce a nonparametric approach to fit multifunctions, allowing to assign a set of output values to a given x. The concept is based on conditional mean shift, which is an easily implemented tool to detect the local maxima of a conditional density function. The methodology is illustrated by environmental data examples.

Citation

Einbeck, J., & Tutz, G. (2006). The fitting of multifunctions: an approach to nonparametric multimodal regression. In A. Rizzi, & M. Vichi (Eds.), COMPSTAT 2006 : proceedings in computational statistics, 17th symposium held in Rome, Italy, 2006 (1251-1258)

Conference Name	COMPSTAT.
Conference Location	Rome, Italy.
Publication Date	Aug 1, 2006
Deposit Date	Jan 29, 2009
Publicly Available Date	Apr 8, 2009
Pages	1251-1258
Series Title	Proceedings in Computational Statistics.
Book Title	COMPSTAT 2006 : proceedings in computational statistics, 17th symposium held in Rome, Italy, 2006.
Keywords	Multi-valued regression, Smoothing, Conditional densities, Conditional mode.
Public URL	https://durham-repository.worktribe.com/output/1161089
Publisher URL	http://www.springer.com/statistics/computational/book/978-3-7908-1708-9