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Large Deviations of χ 2 Divergence Errors on Partitions

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Stochastic Models, Statistics and Their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 122))

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Abstract

We discuss Chernoff-type large deviation results for χ 2 divergence errors on partitions. In contrast to the total variation and the I-divergence, the χ 2-divergence has an unconventional large deviation rate. In this paper we extend the result of Quine and Robinson in Ann. Stat. 13:727–742, 1985 from uniform distribution to arbitrary distribution.

This work was partially supported by the European Union and the European Social Fund through project FuturICT.hu (grant no.: TAMOP-4.2.2.C-11/1/KONV-2012-0013).

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Stoczek u.2, 1521, Budapest, Hungary

    László Györfi

Authors
  1. László Györfi
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Correspondence to László Györfi .

Editor information

Editors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Ansgar Steland

  2. Dept. of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wrocław, Poland

    Ewaryst Rafajłowicz

  3. Inst. of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland

    Krzysztof Szajowski

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Györfi, L. (2015). Large Deviations of χ 2 Divergence Errors on Partitions. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_1

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