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Advances in Data Science and Classification pp 197–204Cite as

On the Asymptotic Normality of a Resubstitution Error Estimate

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Abstract

The resubstitution error estimate for the partitioning classification rule from a sample (X 1,Y 1), (X 2, Y 2), …, (X n , Y n ) is shown to be asymptotically normal under the condition that X has a density f, if the partition consists of rectangles.

The research was supported by the Computer and Automation Institute of the Hungarian Academy of Sciences (MTA SZTAKI).

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References

  • Beirlant, J., Györfi, L. and Lugosi, G. (1994). On the asymptotic normality of the L1- and L2- errors in histogram density estimation. Canadian J. Statistics, 22, 309–318.

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  • Beirlant, J. and Mason, D. (1995). On the asymptotic normality of L p-norms of empirical functionals. Mathematical Methods of Statistics, 4, 1–19.

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  • Devroye, L., Györfi, L. and Lugosi, G. (1996). Probabilistic Theory of Pattern Recognition. Springer Verlag, New York.

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  • Wheeden, R. L. and Zygmund, A. (1977). Measure and Integral. Marcel Dekker Inc., New York, Basel.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science and Information Theory, Technical University of Budapest, 1521, Stoczek u. 2, Budapest, Hungary

    László Györfi & Márta Horváth

Authors
  1. László Györfi
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  2. Márta Horváth
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Editor information

Editors and Affiliations

  1. Dipartimento di Statisticà, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185, Roma, Italia

    Alfredo Rizzi

  2. Dipartimento di Metodi Quantitativi e Teoria Economica, Università “G. D’Annunzio” di Chieti, Viale Pindaro 42, I-65127, Pescara, Italia

    Maurizio Vichi

  3. Institut für Statistik und Wirtschaftsmathematik, Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen, Wüllnerstraße 3, D-52056, Aachen, Germany

    Hans-Hermann Bock

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© 1998 Springer-Verlag Berlin · Heidelberg

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Györfi, L., Horváth, M. (1998). On the Asymptotic Normality of a Resubstitution Error Estimate. In: Rizzi, A., Vichi, M., Bock, HH. (eds) Advances in Data Science and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72253-0_27

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  • DOI: https://doi.org/10.1007/978-3-642-72253-0_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64641-9

  • Online ISBN: 978-3-642-72253-0

  • eBook Packages: Springer Book Archive

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