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Correlation and Marginal Longitudinal Kernel Nonparametric Regression

Chapter
Part of the Lecture Notes in Statistics book series (LNS, volume 179)

Abstract

We consider nonparametric regression in a marginal longitudinal data framework. Previous work ([3]) has shown that the kernel nonparametric regression methods extant in the literature for such correlated data have the discouraging property that they generally do not improve upon methods that ignore the correlation structure entirely. The latter methods are called working independence methods. We construct a two- stage kernel-based estimator that asymptotically uniformly improves upon the working independence estimator. A small simulation study is given in support of the asymptotics.

Keywords

Nonparametric Regression Local Linear Regression Vary Coefficient Model Bias Expression Small Simulation Study 
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]
    F. A. Graybill. Matrices with Applications in Statistic. Wadsworth & Brooks/Cole, 1983.Google Scholar
  2. [2]
    D. R. Hoover, J. A. Rice, C. O. Wu, and Y. Yang. Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, 85:809–822, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    X. Lin and R. J. Carroll. Nonparametric function estimation for clustered data when the predictor is measured without/with error. Journal of the American Statistical Association, 95:520–534, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    J. S. Marron and W. Härdle. Random approximations to some measures of accuracy in nonparametric curve estimatio. Journal of Multivariate Analysis, 20:91–113, 1986.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    M. S. Pepe and D. Couper. Modeling partly conditional means with longitudinal data. Journal of the American Statistical Association, 92:991–998, 1997.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    A. Ruckstuhl, A. H. Welsh, and R. J. Carroll. Nonparametric function estimation of the relationship between two repeatedly measured variables. Statistica Sinica, 10:51–71, 2000.MathSciNetzbMATHGoogle Scholar
  7. [7]
    D. Ruppert. Empirical-bias bandwidths for local polynomial nonparametric regression and density estimatio. Journal of the American Statistical Association, 92:1049–1062, 1997.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    T. A. Severini and J. G. Staniswalis. Quasilikelihood estimation in semiparametric models. Journal of the American Statistical Association, 89:501–511, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    C. J. Wild and T. W. Yee. Additive extensions to generalized estimating equation methods. J. Royal Statist. Soc. B, 58:711–725, 1996.MathSciNetzbMATHGoogle Scholar
  10. [10]
    C. O. Wu, C. T. Chiang, and D. R. Hoover. Asymptotic confidence regions for kernel smoothing of a varying coefficient model with longitudinal data. Journal of the American Statistical Association, 93:1388–1402, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    S. L. Zeger and P. J. Diggle. Semi-parametric models for longitudinal data with application to cd4 cell numbers in hiv seroconverters. Biometrics, 50:689–699, 1994.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  1. 1.London School of EconomicsUK
  2. 2.Heidelberg UniversityGermany
  3. 3.University of MichiganUSA
  4. 4.Texas A&M UniversityUSA

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