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On the Asymptotic Normality of a Resubstitution Error Estimate

  • László Györfi
  • Márta Horváth
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

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.

Key Words

error estimation central limit theorem partitioning classification rule 

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References

  1. 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.CrossRefGoogle Scholar
  2. Beirlant, J. and Mason, D. (1995). On the asymptotic normality of L p-norms of empirical functionals. Mathematical Methods of Statistics, 4, 1–19.Google Scholar
  3. Devroye, L., Györfi, L. and Lugosi, G. (1996). Probabilistic Theory of Pattern Recognition. Springer Verlag, New York.Google Scholar
  4. Wheeden, R. L. and Zygmund, A. (1977). Measure and Integral. Marcel Dekker Inc., New York, Basel.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • László Györfi
    • 1
  • Márta Horváth
    • 1
  1. 1.Dept. of Computer Science and Information TheoryTechnical University of BudapestBudapestHungary

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