 On extensions of Hoeffding’s inequality for panel dataLili Yao and Wenxin Jiang Statistics & Probability Letters, 2012, vol. 82, issue 3, 446-454 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. Keywords: Panel data; Strong mixing; Bosq’s extension; Triplex extension; Convergence rate (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:82:y:2012:i:3:p:446-454 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2011.11.003 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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