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Quantile regression for dynamic partially linear varying coefficient time series models

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  • Lian, Heng

Abstract

In this article, we consider quantile regression method for partially linear varying coefficient models for semiparametric time series modeling. We propose estimation methods based on general series estimation. We establish convergence rates of the estimator and the root-n asymptotic normality of the finite-dimensional parameter in the linear part. We further propose penalization-based method for automatically specifying the linear part of the model as well as performing variable selection, and show the model selection consistency of this approach. We illustrate the performance of estimates using a simulation study.

Suggested Citation

  • Lian, Heng, 2015. "Quantile regression for dynamic partially linear varying coefficient time series models," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 49-66.
    • Handle: RePEc:eee:jmvana:v:141:y:2015:i:c:p:49-66
    DOI: 10.1016/j.jmva.2015.06.013
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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Heng Lian, 2012. "Semiparametric Estimation of Additive Quantile Regression Models by Two-Fold Penalty," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 337-350, March.
    3. Chiang C-T. & Rice J. A & Wu C. O, 2001. "Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 605-619, June.
    4. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
    5. R. L. Eubank & Chunfeng Huang & Y. Muñoz Maldonado & Naisyin Wang & Suojin Wang & R. J. Buchanan, 2004. "Smoothing spline estimation in varying‐coefficient models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 653-667, August.
    6. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    8. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    9. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    10. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    12. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    13. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    14. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    15. Wang, Lan & Kai, Bo & Li, Runze, 2009. "Local Rank Inference for Varying Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1631-1645.
    16. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
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    Cited by:

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    2. Zishu Zhan & Yang Li & Yuhong Yang & Cunjie Lin, 2023. "Model averaging for semiparametric varying coefficient quantile regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 649-681, August.

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