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Generalized Projection Pursuit Regression and Density Approximation

  • Lidia Rejtö
  • Gilbert G. Walter
Conference paper

Abstract

The paper deals with a generalization of the projection pursuit regression algorithm (see P.Huber [3]) in Hilbert space. The strong convergence of the generalized algorithm is first proved and this result then applied to certain spaces in order to define a new density estimator and to obtain results on density approximation.

Keywords

Hilbert Space Sobolev Space Density Approximation Greedy Algorithm Cauchy Sequence 
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]
    Cheng, P., Wu, C.F.J. (1985) Discussion of Projection Pursuit paper of P.J.Huber. The Annals of Statistics 13 490–493.CrossRefGoogle Scholar
  2. [2]
    Csiszár, I., Körner, J. (1981) Information Theory. Academic Press, New York, functions. Z. Wahrscheinlichkeitstheorie verw. Gebiete 55 203–229.Google Scholar
  3. [3]
    Huber, P.J. (1985) Projection Pursuit. The Annals of Statistics 13 435–475.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Jones, L.K. (1987) On a conjecture of Huber concerning the convergence of PP-regression. The Annals of Statistics 15 880–882.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Rudin, W. (1973) Functional Analysis. McGraw, New York.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Lidia Rejtö
    • 1
    • 2
  • Gilbert G. Walter
    • 1
    • 2
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Department of Mathematical SciencesUniversity of Wisconsin-MilwaukeeMilwaukeeUSA

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