Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Academic Staff

Publication details for Jochen Einbeck

Einbeck, Jochen & Tutz, Gerhard (2006), The fitting of multifunctions: an approach to nonparametric multimodal regression, in Rizzi, A. & Vichi, M. eds, Proceedings in Computational Statistics COMPSTAT. Rome, Italy., Physica-Verlag, Rome, 1251-1258.

Author(s) from Durham

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.