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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


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.