$U$-Processes: Rates of Convergence 论文
1987The Annals of Statistics引用 420
Statistical Methods and InferenceBayesian Methods and Mixture ModelsAdvanced Statistical Methods and Models
详细信息
- 发表期刊/会议
- The Annals of Statistics
- 发表日期
- 1987-06-01
- 发表年份
- 1987
关键词
Statistical Methods and InferenceBayesian Methods and Mixture ModelsAdvanced Statistical Methods and Models
摘要
This paper introduces a new stochastic process, a collection of $U$-statistics indexed by a family of symmetric kernels. Conditions are found for the uniform almost-sure convergence of a sequence of such processes. Rates of convergence are obtained. An application to cross-validation in density estimation is given. The proofs adapt methods from the theory of empirical processes.