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Tail Bounds for the Suprema of Empirical Processes over Unbounded Classes of Functions

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Abstract

So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions.

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Authors and Affiliations

  1. Department of Finance, Business School, Nanjing University, Nanjing 210093, P. R. China

    Di Xin Zhang

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  1. Di Xin Zhang
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Correspondence to Di Xin Zhang.

Additional information

This work is supported partially by the National Natural Science Foundation of China (Grant No. 10471061) and the Social Science Foundation of Ministry of Education of China (Grant No. 01JD910001)

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Zhang, D.X. Tail Bounds for the Suprema of Empirical Processes over Unbounded Classes of Functions. Acta Math Sinica 22, 339–345 (2006). https://doi.org/10.1007/s10114-005-0592-7

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  • DOI: https://doi.org/10.1007/s10114-005-0592-7

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