Title:
Modelling-beyond-Regression-Function
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Description: An enormous amount of publications deals with smoothing in the sense of nonpara-
metric regression. However, nearly all of the literature treats the case where predictors
and response are related in the form of a function y = m(x) + noise. In many situa-
tions this simple functional model does not capture adequately the essential relation
between predictor and response. We show by means of speed-°ow diagrams, that
a more general setting may be required, allowing for multifunctions instead of only
functions. It turns out that in this case the conditional modes are more appropriate
for the estimation of the underlying relation than the commonly used mean or the
median. Estimation is achieved using a conditional mean-shift procedure, which is
adapted to the present situation.
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Modelling beyond Regression Function.pdf
