Abstract
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.
Original language | English (US) |
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Pages (from-to) | 556-578 |
Number of pages | 23 |
Journal | Journal of Theoretical Probability |
Volume | 31 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1 2018 |
Keywords
- Exponential inequality
- High-dimensional time series inference
- Mixing conditions
- U-statistics
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty