DISCREPANCY, CHAINING AND SUBGAUSSIAN PROCESSES

• 成果类型: Article
• 署名作者: Mendelson, Shahar
• 署名单位: Technion Israel Institute of Technology; Australian National University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP575
• 发表日期: 2011
• 页码: 985-1026
• 关键词: reconstruction; dimension; entropy; bodies

摘要

We show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs inf((epsilon i)) sup f epsilon F |Sigma(k)(i)=1 epsilon(i) f (X-i)| is asymptotically smaller than the expectation over signs as a function of the dimension k, if the canonical Gaussian process indexed by F is continuous. To that end, we establish a bound on the discrepancy of an arbitrary subset of R-k using properties of the canonical Gaussian process the set indexes, and then obtain quantitative structural information on a typical coordinate projection of a subgaussian class.