The fitting of multifunctions: an approach to nonparametric multimodal regression

Einbeck, Jochen; Tutz, Gerhard

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.

• Presentation Conference Type: Conference Paper (Published)
• Conference Name: COMPSTAT.
• 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