Quadratic inference functions for varying-coefficient models with longitudinal data

Biometrics

Volumn 62, Issue 2, 2006, Pages 379-391

  Qu, Annie ^a   Li, Runze ^b  

^a OREGON STATE UNIVERSITY   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Generalized method of moments; Goodness of fit; Model selection; Penalized spline; Quadratic inference function; Smoothing spline; Varying coefficient model

Indexed keywords

INTELLIGENT SYSTEMS; METHOD OF MOMENTS; PROBABILITY DISTRIBUTIONS; SAMPLING; STATISTICAL TESTS;

ESTIMATION PROCEDURES; GENERALIZED METHOD OF MOMENTS; GOODNESS OF FIT; INFERENCE FUNCTIONS; LONGITUDINAL DATA; MODEL SELECTION; PENALIZED SPLINES; QUADRATIC INFERENCE FUNCTION; SMOOTHING SPLINE; VARYING COEFFICIENT MODEL;

MONTE CARLO METHODS;

ACQUIRED IMMUNE DEFICIENCY SYNDROME; CORRESPONDENCE ANALYSIS; HYPOTHESIS TESTING; INCLUSIVE FITNESS; MONTE CARLO ANALYSIS; STATISTICAL ANALYSIS;

ACQUIRED IMMUNE DEFICIENCY SYNDROME; ARTICLE; CHI SQUARE DISTRIBUTION; LONGITUDINAL STUDY; MONTE CARLO METHOD; REGRESSION ANALYSIS; STATISTICAL ANALYSIS; STATISTICAL MODEL;

EID: 33745271377     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2005.00490.x     Document Type: Article

References (43)

1. Andrews D. W. K. ( 1999). Consistent moment selection procedures for generalized method of moments estimation. Econometrica 67, 543 564.
2. Billingsley P. ( 1995). Probability and Measure, 3rd edition. New York : John Wiley & Sons.
3. Chiang C.-T. Rice J. A., and Wu C. O. ( 2001). Smoothing spline estimation for varying-coefficient models with repeatedly measured dependent variables. Journal of the American Statistical Association 96, 605 619.
4. Crainiceanu C. and Ruppert D. ( 2004). Likelihood ratio tests in linear mixed models with one variance component. Journal of the Royal Statistical Society, Series B 66, 165 185.
5. Crainiceanu C. Ruppert D. Claeskens G., and Wand M. P. ( 2005). Exact likelihood ratio tests for penalised splines. Biometrika 92, 91 103.
6. Crowder M. ( 1995). On the use of a working correlation matrix in using generalised linear models for repeated measures. Biometrika 82, 407 410.
7. Fan J. and Zhang J.-T. ( 2000). Functional linear models for longitudinal data. Journal of the Royal Statistical Society, Series B 62, 303 322.
8. Godambe V. P. ( 1960). An optimum property of regular maximum likelihood estimation. Annals of Mathematical Statistics 31, 1208 1212.
9. Hall P. and Opsomer J. D. ( 2005). Theory for penalised spline regression. Biometrika 92, 105 118.
10. Hansen L. ( 1982). Large sample properties of generalized method of moments estimators. Econometrica 50, 1029 1054.
11. Hart J. D. ( 1997). Nonparametric Smoothing and Lack-of-Fit Tests. New York : Springer.
12. Hastie T. J. and Tibshirani R. J. ( 1993). Varying-coefficient models. Journal of the Royal Statistical Society, Series B 55, 757 776.
13. Heyde C. C. ( 1997). Quasi-Likelihood and Its Application. New York : Springer-Verlag.
14. Hoover D. R. Rice J. A. Wu C. O., and Yang L.-P. ( 1998). Nonparametric smoothing estimates of time-varying-coefficient models with longitudinal data. Biometrika 85, 809 822.
15. Huang J. Z. Wu C. O., and Zhou L. ( 2002). Varying-coefficient models and basis function approximations for the analysis of repeated measurements. Biometrika 89, 111 128.
16. Jarrow R. Ruppert D., and Yu Y. ( 2004). Estimating the interest rate term structure of corporate debt with a semiparametric penalized spline model. Journal of the American Statistical Association 99, 57 66.
17. Kim I. Cohen N., and Carroll R. J. ( 2003). Semiparametric regression splines in matched case-control studies. Biometrics 59, 1158 1169.
18. Liang K. Y. and Zeger S. L. ( 1986). Longitudinal data analysis using generalised linear models. Biometrika 73, 12 22.
19. Lin X. and Carroll R. J. ( 2000). Nonparametric function estimation for clustered data when the predictor is measured without/with error. Journal of the American Statistical Association 95, 520 534.
20. Lin X. Wang N. Welsh A. H., and Carroll R. J. ( 2004). Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data. Biometrika 91, 177 193.
21. Lipsitz S. R. Molenberghs G. Fitzmaurice G. M., and Ibrahim J. ( 2000). GEE with Gaussian estimation of the correlations when data are incomplete. Biometrics 56, 528 536.
22. p. Technometrics 15, 661 675.
23. Martinussen T. and Scheike T. H. ( 2001). Sampling adjusted analysis of dynamic additive regression models for longitudinal data. Scandinavian Journal of Statistics 28, 303 323.
24. Opsomer J. Wang Y., and Yang Y. ( 2001). Nonparametric regression with correlated errors. Statistical Science 16, 134 153.
25. Park C. G. Park T., and Shin D. W. ( 1996). A simple method for generating correlated binary variates. American Statistician 60, 306 310.
26. Pukelsheim F. ( 1993). Optimal Design of Experiments. New York : John Wiley & Sons.
27. Qu A. and Lindsay B. G. ( 2003). Building adaptive estimating equations when inverse-of-covariance estimation is difficult. Journal of the Royal Statistical Society, Series B 65, 127 142.
28. Qu A. Lindsay B. G., and Li B. ( 2000). Improving generalised estimating equations using quadratic inference functions. Biometrika 87, 823 836.
29. Ruppert D. ( 2002). Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics 11, 735 757.
30. Ruppert D. and Carroll R. J. ( 2000). Spatially-adaptive penalties for spline fitting. Australian and New Zealand Journal of Statistics 42, 205 223.
31. Ruppert D. Wand M. P., and Carroll R. J. ( 2003). Semiparametric Regression. New York : Cambridge University Press.
32. Wand M. P. ( 1999). On the optimal amount of smoothing in penalized spline regression. Biometrika 86, 936 940.
33. Wand M. P. ( 2000). A comparison of regression spline smoothing procedures. Computational Statistics 15, 443 462.
34. Wang Y. ( 1998a). Mixed-effects smoothing spline ANOVA. Journal of the Royal Statistical Society, Series B 60, 159 174.
35. Wang Y. ( 1998b). Smoothing spline models with correlated random errors. Journal of the American Statistical Association 93, 341 348.
36. Wang N. ( 2003). Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika 90, 43 52.
37. Wang N. Carroll R., and Lin X. ( 2005). Efficient semiparametric marginal estimation for longitudinal/cluster data. Journal of the American Statistical Association 100, 147 157.
38. Wedderburn R. W. M. ( 1974). Quasi-likelihood functions, generalised linear models, and the Gauss-Newton method. Biometrika 61, 439 447.
39. Wu C. O. and Chiang C.-T. ( 2000). Kernel smoothing on varying-coefficient models with longitudinal dependent variable. Statistica Sinica 10, 433 456.
40. Wu C. O. Chiang C.-T., and Hoover D. R. ( 1998). Asymptotic confidence regions for kernel smoothing of a varying-coefficient model with longitudinal data. Journal of the American Statistical Association 93, 1388 1402.
41. Yu Y. and Ruppert D. ( 2002). Penalized spline estimation for partially linear single-index models. Journal of the American Statistical Association 97, 1042 1054.
42. Yu Y. and Ruppert D. ( 2004). Root-n consistency of penalized spline estimator for partially linear single-index models under general Euclidean space. Statistica Sinica 14, 449 456.
43. Zhang D. ( 2004). Generalized linear mixed models with varying-coefficient for longitudinal data. Biometrics 60, 8 15.