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The fitting of multifunctions : an approach to nonparametric multimodal regression.

Einbeck, J. and Tutz, G. (2006) 'The fitting of multifunctions : an approach to nonparametric multimodal regression.', in COMPSTAT 2006 : proceedings in computational statistics, 17th symposium held in Rome, Italy, 2006. Heidelberg: Physica-Verlag, pp. 1251-1258.


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.

Item Type:Book chapter
Keywords:Multi-valued regression, Smoothing, Conditional densities, Conditional mode.
Full text:(AM) Accepted Manuscript
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Publisher statement:The original publication is available at
Date accepted:No date available
Date deposited:08 April 2009
Date of first online publication:August 2006
Date first made open access:No date available

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