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Ukrainian Mathematical Journal

, Volume 62, Issue 4, pp 588–611 | Cite as

On a measure of integral square deviation with generalized weight for the Rosenblatt–Parzen probability density estimator

  • E. Nadaraya
  • P. Babilua
  • G. Sokhadze
Article

The limit distribution of an integral square deviation with weight in the form of “delta”-functions for the Rosenblatt–Parzen probability density estimator is determined. In addition, the limit power of the goodness-of-fit test constructed by using this deviation is investigated.

Keywords

Limit Distribution Limit Power Generalize Weight Difference Martingale Density Function Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. J. Bickel and M. Rosenblatt, “On some global measures of the deviations of density function estimates,” Ann. Statist., 1, 1071–1095 (1973).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    M. Rosenblatt, “A quadratic measure of deviation of two-dimensional density estimates and a test of independence,” Ann. Statist., 3, 1–14 (1975).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Nadaraya E. A., Nonparametric Estimation of Probability Densities and Regression Curves, Kluwer, Dordrecht (1989).MATHGoogle Scholar
  4. 4.
    P. Hall, “Central limit theorem for integrated square error of multivariate nonparametric density estimators,” J. Multivar. Anal., 14, No. 1, 1–16 (1984).MATHCrossRefGoogle Scholar
  5. 5.
    T. Tony Cai and G. Low Mark, “Nonparametric estimation over shrinking neighborhoods: superefficiency and adaptation,” Ann. Statist., 33, No. 1, 184–213 (2005).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    A. N. Shiryaev, Probability [in Russian], Nauka, Moscow (1989).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • E. Nadaraya
    • 1
  • P. Babilua
    • 1
  • G. Sokhadze
    • 2
  1. 1.Tbilisi State UniversityTbilisiGeorgia
  2. 2.Tsereteli Kutaisi State UniversityKutaisiGeorgia

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