Science in China Series A: Mathematics

, Volume 47, Issue 6, pp 821–830 | Cite as

A local probability exponential inequality for the large deviation of an empirical process indexed by an unbounded class of functions and its application

  • Dixin Zhang


A local probability exponential inequality for the tail of large deviation of an empirical process over an unbounded class of functions is proposed and studied. A new method of truncating the original probability space and a new symmetrization method are given. Using these methods, the local probability exponential inequalities for the tails of large deviations of empirical processes with non-i.i.d. independent samples over unbounded class of functions are established. Some applications of the inequalities are discussed. As an additional result of this paper, under the conditions of Kolmogorov theorem, the strong convergence results of Kolmogorov on sums of non-i.i.d. independent random variables are extended to the cases of empirical processes indexed by unbounded classes of functions, the local probability exponential inequalities and the laws of the logarithm for the empirical processes are obtained.


empirical process large deviation unbounded class of functions local probability exponential inequality 


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Copyright information

© Science in China Press 2004

Authors and Affiliations

  1. 1.Department of FinanceBusiness School, Nanjing UniversityNanjingChina

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