An Exponential Inequality for U-Statistics Under Mixing Conditions

Fang Han ()
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Fang Han: University of Washington

Journal of Theoretical Probability, 2018, vol. 31, issue 1, 556-578

Abstract: 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.

Keywords: U-statistics; Mixing conditions; Exponential inequality; High-dimensional time series inference; 60E15; 60F10 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-016-0722-4

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