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Asymptotic Equivalence for Nonparametric Regression with Non-Regular Errors

Authors
  • Meister, Alexander
  • Reiß, Markus
Type
Preprint
Publication Date
Jan 27, 2011
Submission Date
Jan 27, 2011
Source
arXiv
License
Yellow
External links

Abstract

Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression models and the observation of two independent Poisson point processes which contain the target curve as the support boundary of its intensity function. The intensity of the point processes is of order of the sample size $n$ and involves the jump sizes as well as the design density. The statistical model significantly differs from regression problems with Gaussian or regular errors, which are known to be asymptotically equivalent to Gaussian white noise models.

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