The family of U-statistics plays a fundamental role in statistics. This paper proves a novel exponential inequality for U-statistics under the time series setting. Explicit mixing conditions are given for guaranteeing fast convergence, the bound proves to be analogous to the one under independence, and extension to non-stationary time series is straightforward. The proof relies on a novel decomposition of U-statistics via exploiting the temporal correlatedness structure. Such results are of interest in many fields where high-dimensional time series data are present. In particular, applications to high-dimensional time series inference are discussed.
- Exponential inequality
- High-dimensional time series inference
- Mixing conditions
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty