Identifying shifts between two regression curves
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Date
2019
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Abstract
This article studies the problem whether two convex (concave) regression functions
modelling the relation between a response and covariate in two samples differ by a shift
in the horizontal and/or vertical axis. We consider a nonparametric situation assuming
only smoothness of the regression functions. A graphical tool based on the derivatives
of the regression functions and their inverses is proposed to answer this question and
studied in several examples. We also formalize this question in a corresponding hypothesis
and develop a statistical test. The asymptotic properties of the corresponding
test statistic are investigated under the null hypothesis and local alternatives. In contrast
to most of the literature on comparing shape invariant models, which requires
independent data the procedure is applicable for dependent and non-stationary data.
We also illustrate the finite sample properties of the new test by means of a small
simulation study and a real data example.
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Keywords
comparison of curves, hypothesis testing, nonparametric regression