Penalized quadratic inference functions for single-index models with longitudinal data

Journal of Multivariate Analysis

Volumn 100, Issue 1, 2009, Pages 152-161

  Bai, Yang ^a   Fung, Wing K ^a   Zhu, Zhong Yi ^b  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b FUDAN UNIVERSITY   (China)

Author keywords

46N30; Longitudinal data; P splines; Quadratic inference functions; Single index models

Indexed keywords

EID: 55049140582     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2008.04.004     Document Type: Article

References (28)

1. Stoker T.M. Consistent estimation of scaled coefficients. Econometrica 54 (1986) 1461-1481
2. Härdle W., and Stoker T.M. Investing smoothing multiple regression by the methods of average derivatives. Journal of the American Statistical Association 84 (1989) 986-995
3. Ichimura H. Semiparametric least squares (sls) and weighted sls estimation of single-index models. Journal of Econometrics 58 (1993) 71-120
4. Härdle W., Hall P., and Ichimura H. Optimal smoothing in single-index models. The Annals of Statistics 21 (1993) 157-178
5. Powell J., Stock J., and Stoker T. Semiparametric estimation of index coefficients. Econometrica 57 (1989) 1403-1430
6. Yu Y., and Ruppert D. Penalized smoothing estimation for partially linear single-index models. Journal of the American Statistical Association 97 (2002) 1042-1054
7. Carroll R.J., Fan J., Gijbels I., and Wand M.P. Generalized partially linear single-index models. Journal of the American Statistical Association 92 (1997) 477-489
8. Y. Yu, Penalized spline estimation for generalized partially linear single-index models, 2007. Manuscript http://statqa.cba.uc.edu/~yuy/research/Yu9.pdf
9. Honoré B., and Kyriazidou E. Panel data discrete choice models with lagged dependent variables. Econometrica 68 (2000) 839-874
10. Carro J.M. Estimating dynamic panel data discrete choice models with fixed effects. Journal of Econometrics 140 (2007) 503-528
11. Qu A., and Li R.Z. Quadratic inference functions for varying coefficient models with longitudinal data. Biometrics 62 (2006) 379-391
12. Qu A., Lindsay B.G., and Li B. Improving generalised estimating equations using quadratic inference functions. Biometrika 87 (2000) 823-836
13. Eilers P.H.C., and Marx B.D. Flexible smoothing with b-splines and penalties (with discussion). Statistical Science 11 (1996) 89-121
14. Ruppert D. Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics 11 (2002) 735-757
15. Ruppert D., and Carroll R.J. Spatially-adaptive penalties for spline fitting. Australian and New Zealand Journal of Statistics 42 (2000) 205-223
16. Liang K.L., and Zeger S.L. Longitudinal data analysis using generalised estimating equations. Biometrika 73 (1986) 13-22
17. Bai Y., Zhu Z.Y., and Fung W.K. Partial linear models for longitudinal data based on quadratic inference functions. Scandinavian Journal of Statistics 35 1 (2008) 104-118
18. Prentice R.L., and Zhao L.P. Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics 47 (1991) 825-839
19. Lin X.H., and Carroll R.J. Nonparametric function estimation for clustered data when the predictor is measured without/with error. Journal of the American Statistical Association 95 (2000) 520-534
20. Lin X.H., Wang N., Welsh A.H., and Carroll R.J. Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data. Biometrika 91 (2004) 177-193
21. Crowder M. On the use of a working correlation matrix in using generalised linear models for repeated measures. Biometrika 82 (1995) 407-410
22. Hansen L. Large sample properties of generalized method of moments estimators. Econometrica 50 (1982) 1029-1054
23. Qu A., and Lindsay B.G. Building adaptive estimating equations when inverse-of-covariance estimation is difficult. Journal of the Royal Statistical Society, Series B 65 (2003) 127-142
24. D. Ruppert, R.J. Carroll, Penalized regression splines, Working Paper, Cornell University, School of Operations Research and Industrial Engineering, 1997. Available at: www.orie.cornell.edu/davidr/papers
25. Yuan K.H. A theorem on uniform convergence of stochastic functions with application. Journal of Multivariate Analysis 62 (1997) 100-109
26. Madsen L., and Dalthorp D. Simulating correlated count data. Environmental and Ecological Statistics 14 (2007) 129-148
27. Thall P., and Vail S.C. Some covariance models for longitudinal count data with overdispersion. Biometrics 46 (1990) 657-671
28. Wang Y.-G., Lin X., and Zhu M. Robust estimating functions and bias correction for longitudinal data analysis. Biometrics 61 (2005) 684-691