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Adaptive jump-preserving estimates in varying-coefficient models

Author

Listed:
  • Zhao, Yan-Yong
  • Lin, Jin-Guan
  • Huang, Xing-Fang
  • Wang, Hong-Xia

Abstract

Varying-coefficient models are very important tools to explore the hidden structure between the response variable and its predictors. This article focuses on the estimation of varying-coefficient models with discontinuous coefficient functions. Based on local linear smoothing and jump-preserving regression techniques, an adaptive jump-preserving (AJP) estimation procedure is proposed to estimate the coefficient functions with jumps. This method can automatically accommodate possible jumps of the coefficient functions without knowing the number and locations of jump points or performing any hypothesis tests. Under some mild conditions, the asymptotical properties of the resulting estimators can be established. Furthermore, several numerical studies are conducted to evaluate the finite sample performance of the proposed methodologies. Finally, an application to Australia consumer price index (CPI) data illustrates the validity of the proposed techniques.

Suggested Citation

  • Zhao, Yan-Yong & Lin, Jin-Guan & Huang, Xing-Fang & Wang, Hong-Xia, 2016. "Adaptive jump-preserving estimates in varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 65-80.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:65-80
    DOI: 10.1016/j.jmva.2016.03.005
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    References listed on IDEAS

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    1. Wang, Qihua & Zhang, Riquan, 2009. "Statistical estimation in varying coefficient models with surrogate data and validation sampling," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2389-2405, November.
    2. Tang, Yanlin & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in quantile varying coefficient models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 435-449.
    3. Weihua Zhao & Riquan Zhang & Jicai Liu, 2013. "Robust variable selection for the varying coefficient model based on composite L 1 -- L 2 regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 2024-2040, September.
    4. 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.
    5. Zhao, Yan-Yong & Lin, Jin-Guan & Xu, Pei-Rong & Ye, Xu-Guo, 2015. "Orthogonality-projection-based estimation for semi-varying coefficient models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 204-221.
    6. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    7. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    8. Tang, Yanlin & Song, Xinyuan & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in high-dimensional quantile varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 115-132.
    9. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    10. Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood for a Varying Coefficient Model With Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 642-654, June.
    11. 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.
    12. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2005. "Nonparametric estimation of structural change points in volatility models for time series," Journal of Econometrics, Elsevier, vol. 126(1), pages 79-114, May.
    13. Peixin Zhao & Liugen Xue, 2011. "Variable selection for varying coefficient models with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 231-245, September.
    14. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
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    Cited by:

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    2. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    3. Yan-Yong Zhao & Jin-Guan Lin & Hong-Xia Wang & Xing-Fang Huang, 2017. "Jump-detection-based estimation in time-varying coefficient models and empirical applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 574-599, September.
    4. Han, Zhong-Cheng & Lin, Jin-Guan & Zhao, Yan-Yong, 2020. "Adaptive semiparametric estimation for single index models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    5. Zhao, Yan-Yong & Lin, Jin-Guan, 2019. "Estimation and test of jump discontinuities in varying coefficient models with empirical applications," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 145-163.
    6. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.

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