Generalized Projection Pursuit Regression and Density Approximation

  • Lidia Rejtö
  • Gilbert G. Walter
Conference paper


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.


Hilbert Space Sobolev Space Density Approximation Greedy Algorithm Cauchy Sequence 
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    Csiszár, I., Körner, J. (1981) Information Theory. Academic Press, New York, functions. Z. Wahrscheinlichkeitstheorie verw. Gebiete 55 203–229.Google Scholar
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    Huber, P.J. (1985) Projection Pursuit. The Annals of Statistics 13 435–475.MathSciNetMATHCrossRefGoogle Scholar
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    Jones, L.K. (1987) On a conjecture of Huber concerning the convergence of PP-regression. The Annals of Statistics 15 880–882.MathSciNetMATHCrossRefGoogle Scholar
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    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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