Testing for symmetries in multivariate inverse problems
Loading...
Date
2011-04-27
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We propose a test for shape constraints which can be expressed by transformations of the
coordinates of multivariate regression functions. The method is motivated by the constraint
of symmetry with respect to some unknown hyperplane but can easily be generalized to other
shape constraints of this type or other semi-parametric settings. In a first step, the unknown
parameters are estimated and in a second step, this estimator is used in the L2-type test
statistic for the shape constraint. We consider the asymptotic behaviour of the estimated
parameter and show, that it converges with parametric rate if the shape constraint is true.
Moreover we derive the asymptotic distribution of the test statistic under the null hypothesis
and furthermore propose a bootstrap test based on the residual bootstrap. In a simulation
study we investigate the finite sample performance of the estimator as well as the bootstrap
test.
Description
Table of contents
Keywords
deconvolution, goodness-of-fit, inverse problems, semi-parametric regression, symmetry