Asymptotic approximation of nonparametric regression experiments with unknown variances

• 成果类型: Article
• 署名作者: Carter, Andrew V.
• 署名单位: University of California System; University of California Santa Barbara
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001613
• 发表日期: 2007
• 页码: 1644-1673
• 关键词: wavelet shrinkage; heteroscedasticity; EQUIVALENCE

摘要

Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown nuisance parameter. We establish an asymptotic approximation to the nonparametric regression experiment when the value of the variance is an additional parameter to be estimated or tested. This asymptotically equivalent experiment has two components: the first contains all the information about the variance and the second has all the information about the mean. The result can be extended to regression problems where the variance varies slowly from observation to observation.