On extensions of Hoeffding's inequality for panel data

Lili Yao*, Wenxin Jiang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Hoeffding's inequality provides a probability bound for the deviation between the average of n independent bounded random variables and its mean. This paper introduces two inequalities that extend Hoeffding's inequality to panel data, which consists of several mutually independent sequences of dependent data with strong mixing or with a dependence structure being even more general than strong mixing. One is denoted as the Bosq's Extension which is an extension of Bosq's inequality(Bosq, 1993) to panel data and the other one is called the Triplex Extension, which extends the Triplex inequality(Jiang, 2009) to panel data. The Bosq's Extension provides a tighter upper probability bound, while the Triplex Extension is more relaxed in assumption allowing unboundedness and more general dependence than strong mixing. We also apply these two inequalities to establish the convergence rate of empirical risk minimization for high dimensional panel data with variable selection.

Original languageEnglish (US)
Pages (from-to)446-454
Number of pages9
JournalStatistics and Probability Letters
Volume82
Issue number3
DOIs
StatePublished - Mar 1 2012

Keywords

  • Bosq's extension
  • Convergence rate
  • Panel data
  • Strong mixing
  • Triplex extension

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

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