An Exponential Inequality for U-Statistics Under Mixing Conditions

Fang Han

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)556-578
Number of pages23
JournalJournal of Theoretical Probability
Volume31
Issue number1
DOIs
StatePublished - 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

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