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 Web site:||http://www.springer.com/statistics/computational/book/978-3-7908-1708-9|
|Publisher statement:||The original publication is available at www.springerlink.com|
|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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