Robust estimation in generalized partial linear models for clustered data

Journal of the American Statistical Association

Volumn 100, Issue 472, 2005, Pages 1176-1184

  He, Xuming ^a   Fung, Wing K ^b   Zhu, Zhongyi ^c  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

B spline; Estimating equation; Generalized linear model; Longitudinal data; Robustness

Indexed keywords

EID: 29144468067     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214505000000277     Document Type: Article

References (33)

1. Bianco, A. M., and Yohai, V. J. (1996), "Robust Estimation in the Logistic Regression," in Robust Statistics, Data Analysis, and Computer-Intensive Methods: In Honor of Peter Huber's 60th Birthday, ed. H. Rieder, New York: Springer-Verlag, pp. 17-34.
2. Cantoni, E. (2002), "A Robust Approach to Longitudinal Data Analysis," technical report, University of Geneva, Dept. of Econometrics.
3. Cantoni, E., and Ronchetti, E. (2001), "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, 96, 1022-1030.
4. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A. (1986), Robust Statistics: The Approach Based on Influence Functions, New York: Wiley.
5. Härdle, W., Mammen, E., and Müller, M. (1998), "Testing Parametric versus Semiparametric Modelling in Generalized Linear Models," Journal of the American Statistical Association, 93, 1461-1474.
6. He, X., Fu, B., and Fung, W. K. (2003), "Median Regression of Longitudinal Data," Statistics in Medicine, 23, 3655-3669.
7. He, X., and Shi, P. (1996), "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, 58, 162-181.
8. He, X., Simpson, D. G., and Wang, G. (2000), "Breakdown Points of t-Type Regression Estimators," Biometrika, 87, 675-687.
9. He, X., Zhu, Z. Y., and Fung, W. K. (2002), "Estimation in a Semiparametric Model for Longitudinal Data With Unspecified Dependence Structure," Biometrika, 89, 579-590.
10. Heckman, N. E. (1986), "Spline Smoothing in a Partly Linear Model," Journal of the Royal Statistical Society, Ser. B, 48, 244-248.
11. Heyde, C. C., and Morton, R. (1998), "Multiple Roots in General Estimating Equations," Biometrika, 85, 954-959.
12. Jureckova, J., and Portnoy, S. (1987), "Asymptotics for One-Step M-Estimators in Regression With Application to Combining Efficiency and High Breakdown Point," Communications in Statistics, Part A - Theory and Methods, 16, 2187-2199.
13. Künsch, H., Stefanski, L., and Carroll, R. (1989), "Conditionally Unbiased Bounded-Influence Estimation in General Regression Models With Applications to Generalized Linear Models," Journal of the American Statistical Association, 84, 460-466.
14. Liang, K. Y., and Zeger, S. L. (1986), "Longitudinal Data Analysis Using Generalized Linear Models," Biometrika, 73, 13-22.
15. Lin, X., and Carroll, R. J. (2001a), "Semiparametric Regression for Clustered Data," Biometrika, 88, 1179-1185.
16. _ (2001b), "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, 96, 1045-1056.
17. McCullagh, P., and Nelder, J. (1989), Generalized Linear Models (2nd ed.), London: Chapman & Hall.
18. Müller, M. (2001), "Estimation and Testing in Generalized Partial Linear Models: A Comparative Study," Statistics and Computing, 11, 299-309.
19. Pan, W. (2002), "Goodness-of-Fit Tests for GEE With Correlated Binary Data," Scandinavian Journal of Statistics, 29, 101-110.
20. Preisser, J. S., and Qaqish, B. F. (1999), "Robust Regression for Clustered Data With Application to Binary Responses," Biometrics, 55, 574-579.
21. Rice, J. (1986), "Convergence Rates for Partially Splined Models," Statistics and Probability Letters, 4, 203-208.
22. Rousseeuw, P., and Van Driessen, K. (1999), "A Fast Algorithm for the Minimum Covariance Determinant Estimator," Technometrics, 44, 212-223.
23. Schumaker, L. L. (1981), Spline Functions, New York: Wiley.
24. Severini, T. A., and Staniswalis, J. G. (1994), "Quasi-Likelihood Estimation in Semiparametric Models," Journal of the American Statistical Association, 89, 501-511.
25. Sinha, S. K. (2004), "Robust Analysis of Generalized Linear Mixed Models," Journal of the American Statistical Association, 99, 451-460.
26. Speckman, P. (1988), "Kernel Smoothing in Partial Linear Models," Journal of the Royal Statistical Society, Ser. B, 50, 413-436.
27. Stefanski, L., Carroll, R., and Ruppert, D. (1986), "Bounded Score Functions for Generalized Linear Models," Biometrika, 73, 413-424.
28. Stone, C. (1985), "Additive Regression and Other Nonparametric Models," The Annals of Statistics, 13, 689-705.
29. Wang, N. (2003), "Marginal Nonparametric Kernel Regression Accounting for Within-Subject Correlation," Biometrika, 90, 43-52.
30. Welsh, A. H., Lin, X., and Carroll, R. J. (2002), "Marginal Longitudinal Nonparametric Regression: Locality and Efficiency of Spline and Kernel Methods," Journal of the American Statistical Association, 97, 482-493.
31. Welsh, A. H., and Richardson, A. M. (1997), "Approaches to the Robust Estimation of Mixed Models," in Handbook of Statistics, Vol. 15, eds. G. S. Maddala and C. R. Rao, Amsterdam: Elsevier, pp. 343-385.
32. Yau, K. K. W., and Kuk, A. Y. C. (2002), "Robust Estimation in Generalized Linear Mixed Models," Journal of the Royal Statistical Society, Ser. B, 64, 101-117.
33. Zeger, S. L., and Karim, M. R. (1991), "Generalized Linear Models With Random Effects: A Gibbs Sampling Approach," Journal of the American Statistical Association, 86, 79-86.