$U$-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.