Limit theorems for dependent \(U\)-statistics. (English) Zbl 1105.62047
Bertail, Patrice (ed.) et al., Dependence in probability and statistics. New York, NY: Springer (ISBN 0-387-31741-4/pbk). Lecture Notes in Statistics 187, 65-86 (2006).
This paper gives a very concise summary of limit theorems for U-statistics and the related von Mises statistics based on independent observations. The paper then surveys some recent results for U-statistics based on weakly dependent observations generated by functionals of absolutely regular processes. Specifically the U-statistic ergodic theorem, the central limit theorem and empirical U-processes are reviewed.
For the entire collection see [Zbl 1092.60002].
For the entire collection see [Zbl 1092.60002].
Reviewer: Neville Weber (Sydney)
MSC:
62G20 | Asymptotic properties of nonparametric inference |
60F05 | Central limit and other weak theorems |
60F17 | Functional limit theorems; invariance principles |