An Exponential Inequality for U-Statistics Under Mixing Conditions

作者：Han Fang^*

来源：Journal of Theoretical Probability, 2018, 31(1): 556-578.

DOI：10.1007/s10959-016-0722-4

• U-statistics
• Mixing conditions
• Exponential inequality
• High-dimensional time series inference

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.

• 出版日期2018-3