On extensions of Hoeffding’s inequality for panel data
AbstractHoeffding’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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 82 (2012)
Issue (Month): 3 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Hsiao,Cheng, 2003.
"Analysis of Panel Data,"
Cambridge University Press, number 9780521818551, October.
- Jiang, Wenxin & Tanner, Martin A., 2010. "Risk Minimization For Time Series Binary Choice With Variable Selection," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1437-1452, October.
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