GAUSSIAN CHARACTERIZATION OF UNIFORM DONSKER CLASSES OF FUNCTIONS

• 成果类型: Article
• 署名作者: GINE, E; ZINN, J
• 署名单位: City University of New York (CUNY) System; College of Staten Island (CUNY); Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990450
• 发表日期: 1991
• 页码: 758-782
• 关键词: central limit-theorem; banach-spaces; Empirical Processes

摘要

It is proved that, for classes of functions F satisfying some measurability, the empirical processes indexed by F and based on P member-of P(S) satisfy the central limit theorem uniformly in P member-of P(S) if and only if the P-Brownian bridges G(P) indexed by F are sample bounded and rho-p uniformly continuous uniformly in P member-of P(S). Uniform exponential bounds for empirical processes indexed by universal bounded Donsker and uniform Donsker classes of functions are also obtained.