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Estimation of a Functional Single Index Model

Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

Single index models have been mostly studied as an alternative dimension reduction technique for nonparametric regression with multivariate covariates. The index parameter appearing in the model summarizes the effect of the covariates in a finite dimensional vector. We consider an extension to a functional single index parameter which is of infinite dimensional, as a summary of the effect of a functional explanatory variable on a scalar response variable and propose a new estimator based on the idea of functional derivative estimation.

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References

  1. 1.
    Delaigle, A., Hall, P.: Defining probability density for a distribution of random functions. Ann. Stat. 38 (2), 1171–1193 (2010)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Hall, P.,Müller, H. G., Yao, F.: Estimation of functional derivatives. Ann. Stat. 37, 3307–3329 (2009)MATHGoogle Scholar
  3. 3.
    H¨ardle, W., Stoker, T. M.: Investing smooth multiple regression by the method of average derivatives. J. Am. Stat. Assoc. 84 (408), 986–995 (1989)Google Scholar
  4. 4.
    Jiang, C.-R., Wang, J.-L.: Functional single index models for longitudinal data. Ann. Stat. 39 (1), 362–388 (2011)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Frédéric Ferraty
    • 1
  • Juhyun Park
    • 2
  • Philippe Vieu
    • 1
  1. 1.Institut de Mathématiques de ToulouseToulouseFrance
  2. 2.Lancaster UniversityLancasterU.K.

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