RATES OF CONVERGENCE FOR EMPIRICAL PROCESSES OF STATIONARY MIXING SEQUENCES

• 成果类型: Article
• 署名作者: YU, B
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988849
• 发表日期: 1994
• 页码: 94-116
• 关键词: limit-theorems; sums

摘要

Classical empirical process theory for Vapnik-Cervonenkis classes deals mainly with sequences of independent variables. This paper extends the theory to stationary sequences of dependent variables. It establishes rates of convergence for beta-mixing and phi-mixing empirical processes indexed by classes of functions. The method of proof depends on a coupling of the dependent sequence with sequences of independent blocks, to which the classical theory can be applied. A uniform O(n(-s/(1+s))) rate of convergence over V-C classes is established for sequences whose mixing coefficients decay slightly faster than O(n(-s)).