文章基本信息

标题：On signal detection and confidence sets for low rank inference problems
本地全文：下载
作者：Alexandra Carpentier ; Richard Nickl
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2015
卷号：9
期号：2
页码：2675-2688
DOI：10.1214/15-EJS1087
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider the signal detection problem in the Gaussian design trace regression model with low rank alternative hypotheses. We derive the precise (Ingster-type) detection boundary for the Frobenius and the nuclear norm. We then apply these results to show that honest confidence sets for the unknown matrix parameter that adapt to all low rank sub-models in nuclear norm do not exist. This shows that recently obtained positive results in [5] for confidence sets in low rank recovery problems are essentially optimal.