Asymptotic equivalence for nonparametric regression with non-regular errors

• 成果类型: Article
• 署名作者: Meister, Alexander; Reiss, Markus
• 署名单位: University of Rostock; Humboldt University of Berlin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0396-x
• 发表日期: 2013
• 页码: 201-229
• 关键词: information; statistics

摘要

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.