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Probability Theory and Related Fields

, Volume 155, Issue 1–2, pp 201–229 | Cite as

Asymptotic equivalence for nonparametric regression with non-regular errors

  • Alexander MeisterEmail author
  • Markus Reiß
Article

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.

Keywords

Extreme value statistics Frontier estimation Le Cam distance Le Cam equivalence Poisson point processes 

Mathematics Subject Classification (2010)

62B15 62G08 62M30 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut für MathematikUniversität RostockRostockGermany
  2. 2.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany

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