IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v149y2016icp65-80.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1630001X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.03.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    3. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    4. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    5. 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).
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Chaohui Guo & Hu Yang & Jing Lv, 2017. "Robust variable selection in high-dimensional varying coefficient models based on weighted composite quantile regression," Statistical Papers, Springer, vol. 58(4), pages 1009-1033, December.
    4. Ngai Hang Chan & Linhao Gao & Wilfredo Palma, 2022. "Simultaneous variable selection and structural identification for time‐varying coefficient models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 511-531, July.
    5. 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.
    6. Feng, Sanying & He, Wenqi & Li, Feng, 2020. "Model detection and estimation for varying coefficient panel data models with fixed effects," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    7. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    8. Lijie Gu & Li Wang & Wolfgang Härdle & Lijian Yang, 2014. "A simultaneous confidence corridor for varying coefficient regression with sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 806-843, December.
    9. Kangning Wang, 2018. "Variable selection for spatial semivarying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 323-351, April.
    10. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.
    11. Jun Jin & Tiefeng Ma & Jiajia Dai, 2021. "New efficient spline estimation for varying-coefficient models with two-step knot number selection," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 693-712, July.
    12. Weihua Zhao & Weiping Zhang & Heng Lian, 2020. "Marginal quantile regression for varying coefficient models with longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 213-234, February.
    13. Zhao, Weihua & Jiang, Xuejun & Lian, Heng, 2018. "A principal varying-coefficient model for quantile regression: Joint variable selection and dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 269-280.
    14. 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.
    15. Wang, Qihua & Xue, Liugen, 2011. "Statistical inference in partially-varying-coefficient single-index model," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 1-19, January.
    16. Kangning Wang & Xiaofei Sun, 2020. "Efficient parameter estimation and variable selection in partial linear varying coefficient quantile regression model with longitudinal data," Statistical Papers, Springer, vol. 61(3), pages 967-995, June.
    17. Wongsa-art, Pipat & Kim, Namhyun & Xia, Yingcun & Moscone, Francesco, 2024. "Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    18. Koo, Bonsoo & Seo, Myung Hwan, 2015. "Structural-break models under mis-specification: Implications for forecasting," Journal of Econometrics, Elsevier, vol. 188(1), pages 166-181.
    19. Chen, Bin & Maung, Kenwin, 2023. "Time-varying forecast combination for high-dimensional data," Journal of Econometrics, Elsevier, vol. 237(2).
    20. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:65-80. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.