MANIFOLD ESTIMATION AND SINGULAR DECONVOLUTION UNDER HAUSDORFF LOSS

• 成果类型: Article
• 署名作者: Genovese, Christopher R.; Perone-Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry
• 署名单位: Carnegie Mellon University; Sapienza University Rome
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS994
• 发表日期: 2012
• 页码: 941-963
• 关键词: convergence; rates

摘要

We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.