文章基本信息

标题：Honest and adaptive confidence sets in $L_{p}$
本地全文：下载
作者：Alexandra Carpentier
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：2875-2923
DOI：10.1214/13-EJS867
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider the problem of constructing honest and adaptive confidence sets in $L_{p-loss (with $p\geq1$ and $p<\infty$) over sets of Sobolev-type classes, in the setting of non-parametric Gaussian regression. The objective is to adapt the diameter of the confidence sets with respect to the smoothness degree of the underlying function, while ensuring that the true function lies in the confidence interval with high probability. When $p\geq2$, we identify two main regimes, (i) one where adaptation is possible without any restrictions on the model, and (ii) one where critical regions have to be removed. We also prove by a matching lower bound that the size of the regions that we remove can not be chosen significantly smaller. These regimes are shown to depend in a qualitative way on the index $p$, and a continuous transition from $p=2$ to $p=\infty$ is exhibited.
关键词：Non-parametric confidence sets;non-parametric testing problems.