Advertisement

Functional Varying Coefficient Models

  • Hans-Georg Müller
  • Damla Şentürk
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

Functional varying coefficient models provide a versatile and flexible analysis tool for relating longitudinal responses to longitudinal predictors. Two key innovations are: Representing the varying coefficient functions through auto- and cross-covariances of the underlying stochastic processes; and including history effects through a smooth history index function. This presentation is a review of the paper Şentürk and Müller (2010).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cardot, H., Ferraty, F., Sarda, P.: Spline estimators for the functional linear model. Stat. Sinica 13, 571–591 (2003)MathSciNetMATHGoogle Scholar
  2. 2.
    Chiang, C. T., Rice, J. A., Wu, C. O.: Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. J. Am. Stat. Assoc. 96, 605–619 (2001)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Cleveland, W. S., Grosse, E., Shyu, W. M.: Local regression models. In: Chambers, J. M., Hastie, T. J. (eds.) Statistical Models in S, pp. 309–376, Wadsworth & Brooks, Pacific Grove.Google Scholar
  4. 4.
    Cuevas, A., Febrero, M., Fraiman, R.: Linear functional regression: the case of fixed design and functional response. Canad. J. Stat. 33, 285–300 (2002)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis. Springer, New York (2006)MATHGoogle Scholar
  6. 6.
    Huang, J. Z., Wu, C. O., Zhou, L.: Polynomial spline estimation and inference for varying coefficient models with longitudinal data. Stat. Sinica 14, 763–788 (2004)MathSciNetMATHGoogle Scholar
  7. 7.
    James, G., Hastie, T. J., Sugar, C. A.: Principal component models for sparse functional data. Biometrika 87, 587–602 (2000)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Malfait, N., Ramsay, J. O.: The historical functional linear model. Canad. J. Stat. 31, 115–128 (2003)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    M¨uller, H.G., Yao, F.: Functional additivemodels. J. Am. Stat. Assoc. 103, 1534–1544 (2008)Google Scholar
  10. 10.
    M¨uller, H. G., Zhang, Y.: Time-varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories. Biometrics 61, 1064–1075 (2005)Google Scholar
  11. 11.
    Ramsay, J. O., Silverman, B. W.: Functional Data Analysis (Second Edition). Springer, New York (2005)Google Scholar
  12. 12.
    Ramsay, J. O., Dalzell, C. J.: Some tools for functional data analysis. J. Roy. Stat. Soc. B 53, 539–572 (1991)MathSciNetMATHGoogle Scholar
  13. 13.
    S¸entürk, D., Müller, H. G.: Generalized varying coefficient models for longitudinal data. Biometrika 95, 653–666 (2008)Google Scholar
  14. 14.
    S¸entürk, D., Müller, H.G.: Functional varying coefficient models for longitudinal data. J. Am. Stat. Assoc. 105, 1256–1264 (2010)Google Scholar
  15. 15.
    Wu, C. O., Chiang, C. T.: Kernel smoothing on varying coefficient models with longitudinal dependent variable. Stat. Sinica 10, 433–456 (2000)MathSciNetMATHGoogle Scholar
  16. 16.
    Yao, F.,Müller, H. G.,Wang, J. L.: Functional linear regression analysis for longitudinal data. Ann. Stat. 33, 2873–2903 (2005a)MATHCrossRefGoogle Scholar
  17. 17.
    Yao, F., Müller, H.G., Wang, J.L.: Functional data analysis for sparse longitudinal data. J. Am. Stat. Assoc. 100, 577–590 (2005b)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.University of CaliforniaDavisUSA
  2. 2.Penn State UniversityUniversity ParkUSA

Personalised recommendations