OPTIMAL RATES OF CONVERGENCE FOR CONVEX SET ESTIMATION FROM SUPPORT FUNCTIONS

• 成果类型: Article
• 署名作者: Guntuboyina, Adityanand
• 署名单位: University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS959
• 发表日期: 2012
• 页码: 385-411
• 关键词: maximum-likelihood-estimation; log-concave density; limit distribution-theory; line measurements; reconstruction; regression; entropy

摘要

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator. Both fixed and random designs are considered.