LIMIT-THEOREMS FOR U-PROCESSES

• 成果类型: Article
• 署名作者: ARCONES, MA; GINE, E
• 署名单位: University of Connecticut
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989128
• 发表日期: 1993
• 页码: 1494-1542
• 关键词: Empirical Processes; symmetric statistics; inequalities; CONVERGENCE

摘要

Necessary and sufficient conditions for the law of large numbers and sufficient conditions for the central limit theorem for U-processes are given. These conditions are in terms of random metric entroPies. The CLT and LLN for VC subgraph classes of functions as well as for classes satisfying bracketing conditions follow as consequences of the general results. In particular, Liu's simplicial depth Process satisfies both the LLN and the CLT. Among the techniques used, randomization, decoupling inequalities, integrability of Gaussian and Rademacher chaos and exponential inequalities for U-statistics should be mentioned.