Abstract
Stimulated by a study in Bangladesh about the first birth interval, we propose a semivarying-coefficient model for cluster data analysis. We consider the estimation procedure for the proposed model and establish the asymptotic results of the proposed estimators. Furthermore, we employ the cross-validation (CV) to identify the constant coefficients. The associated asymptotic properties are rigorously examined. Simulation studies are conducted to investigate the performance of the proposed estimation and the CV-based model selection procedure for finite sample size. Finally, our methods are used to analyse the aforementioned data set to explore how several factors affect the first birth interval in Bangladesh.
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References
Chiou J.-M., Müller H-G. (2005) Estimated estimating equations: semiparametric inference for clustered/longitudinal data. Journal of the Royal Statistical Society, Series B 67: 531–553
Demidenko E. (2004) Mixed models: Theory and applications. Wiley, Hoboken
Fan J., Huang T. (2005) Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli 11: 1031–1057
Fan J., Li R. (2004) New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. Journal of the American Statistical Association 99: 710–723
Fan J., Wu Y. (2008) Semiparametric estimation of covariance matrixes for longitudinal data. Journal of the American Statistical Association 103: 1520–1533
Fan J., Zhang W. (1999) Statistical estimation in varying coefficient models. The Annals of Statistics 27: 1491–1518
Fan J., Zhang J.-T. (2000a) Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society, Series B 62: 303–322
Fan J., Zhang W. (2000b) Simultaneous confidence bands and hypothesis testing in varying-coefficient models. Scandinavian Journal of Statistics 27: 715–731
Fan J., Huang T., Li R. (2007) Analysis of longitudinal data with semiparametric estimation of covariance function. Journal of American Statistical Association 102: 632–641
Li J., Zhang W. (2011) A semiparametric threshold model for censored longitudinal data analysis. Journal of the American Statistical Association 106: 685–696
Li J., Zhang W., Wu Z. (2011) Optimal zone for bandwidth selection in semiparametric models. Journal of Nonparametric Statistics 23: 701–717
Mitra, S. N., Al-Sabir, A., Cross, A. R., Jamil, K. (1997). Bangladesh and Demographic Health Survey 1996–1997. Dhaka and Calverton, MD: National Institute of Population Research and Training (NIPORT), Mitra and Associates, and Macro International Inc. Bangladesh.
Sun Y., Zhang W., Tong H. (2007) Estimation of the covariance matrix of random effects in longitudinal studies. The Annals of Statistics 35: 2795–2814
Wang L., Bo K., Li R. (2009) Local rank inference for varying coefficient models. Journal of American Statistical Association 104: 1631–1645
Xia Y., Zhang W., Tong H. (2004) Efficient estimation for semivarying-coefficient models. Biometrika 91: 661–681
Zhang W., Lee S. Y. (2000) Variable bandwidth selection in varying-coefficient models. Journal of Multivariate Analysis 74: 116–134
Zhang W., Lee S. Y., Song X. (2002) Local polynomial fitting in semivarying coefficient models. Journal of Multivariate Analysis 82: 166–188
Zhang W., Fan J., Sun Y. (2009) A semiparametric model for cluster data. Annals of Statistics 37: 2377–2408
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Sun, Y., Li, J. & Zhang, W. Estimation and model selection in a class of semiparametric models for cluster data. Ann Inst Stat Math 64, 835–856 (2012). https://doi.org/10.1007/s10463-011-0342-9
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DOI: https://doi.org/10.1007/s10463-011-0342-9