Functional Varying Coefficient Models

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Recent Advances in Functional Data Analysis and Related Topics

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

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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).

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References

  1. Cardot, H., Ferraty, F., Sarda, P.: Spline estimators for the functional linear model. Stat. Sinica 13, 571–591 (2003)

    MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. Cuevas, A., Febrero, M., Fraiman, R.: Linear functional regression: the case of fixed design and functional response. Canad. J. Stat. 33, 285–300 (2002)

    Article  MathSciNet  Google Scholar 

  5. Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis. Springer, New York (2006)

    MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  7. James, G., Hastie, T. J., Sugar, C. A.: Principal component models for sparse functional data. Biometrika 87, 587–602 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  8. Malfait, N., Ramsay, J. O.: The historical functional linear model. Canad. J. Stat. 31, 115–128 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. M¨uller, H.G., Yao, F.: Functional additivemodels. J. Am. Stat. Assoc. 103, 1534–1544 (2008)

    Google Scholar 

  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. Ramsay, J. O., Silverman, B. W.: Functional Data Analysis (Second Edition). Springer, New York (2005)

    Google Scholar 

  12. Ramsay, J. O., Dalzell, C. J.: Some tools for functional data analysis. J. Roy. Stat. Soc. B 53, 539–572 (1991)

    MathSciNet  MATH  Google Scholar 

  13. S¸entürk, D., Müller, H. G.: Generalized varying coefficient models for longitudinal data. Biometrika 95, 653–666 (2008)

    Google Scholar 

  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. Wu, C. O., Chiang, C. T.: Kernel smoothing on varying coefficient models with longitudinal dependent variable. Stat. Sinica 10, 433–456 (2000)

    MathSciNet  MATH  Google Scholar 

  16. Yao, F.,Müller, H. G.,Wang, J. L.: Functional linear regression analysis for longitudinal data. Ann. Stat. 33, 2873–2903 (2005a)

    Article  MATH  Google Scholar 

  17. Yao, F., Müller, H.G., Wang, J.L.: Functional data analysis for sparse longitudinal data. J. Am. Stat. Assoc. 100, 577–590 (2005b)

    Article  MATH  Google Scholar 

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Correspondence to Hans-Georg Müller .

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Müller, HG., Şentürk, D. (2011). Functional Varying Coefficient Models. In: Ferraty, F. (eds) Recent Advances in Functional Data Analysis and Related Topics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2736-1_35

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