IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v74y2000i1p116-134.html
   My bibliography  Save this article

Variable Bandwidth Selection in Varying-Coefficient Models

Author

Listed:
  • Zhang, Wenyang
  • Lee, Sik-Yum

Abstract

The varying-coefficient model is an attractive alternative to the additive and other models. One important method in estimating the coefficient functions in this model is the local polynomial fitting approach. In this approach, the choice of bandwidth is crucial. If the unknown curve is spatial homogeneous, a constant bandwidth is sufficient. However, for estimating curves with a more complicated structure, a variable bandwidth is needed. The present article focuses on a variable bandwidth selection procedure, and provides the conditional bias and the conditional variance of the estimator, the convergence rate of the bandwidth, and the asymptotic distribution of its error relative to the theoretical optimal variable bandwidth.

Suggested Citation

  • Zhang, Wenyang & Lee, Sik-Yum, 2000. "Variable Bandwidth Selection in Varying-Coefficient Models," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 116-134, July.
    • Handle: RePEc:eee:jmvana:v:74:y:2000:i:1:p:116-134
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(99)91883-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Lu, Zhan-Qian, 1996. "Multivariate Locally Weighted Polynomial Fitting and Partial Derivative Estimation," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 187-205, November.
    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. Shang, Suoping & Zou, Changliang & Wang, Zhaojun, 2012. "Local Walsh-average regression for semiparametric varying-coefficient models," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1815-1822.
    2. Jianqing Fan & Wenyang Zhang, 2015. "Discussion," International Statistical Review, International Statistical Institute, vol. 83(1), pages 65-68, April.
    3. Jialiang Li & Wenyang Zhang & Zhengxiao Wu, 2011. "Optimal zone for bandwidth selection in semiparametric models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 701-717.
    4. Fernando Rios-Avila, 2019. "A Semi-Parametric Approach to the Oaxaca–Blinder Decomposition with Continuous Group Variable and Self-Selection," Econometrics, MDPI, vol. 7(2), pages 1-29, June.
    5. Jingxin Zhao & Heng Peng & Tao Huang, 2018. "Variance estimation for semiparametric regression models by local averaging," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 453-476, June.
    6. Yan Sun & Jialiang Li & Wenyang Zhang, 2012. "Estimation and model selection in a class of semiparametric models for cluster data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 835-856, August.
    7. Delis, Manthos D. & Tran, Kien C. & Tsionas, Efthymios G., 2012. "Quantifying and explaining parameter heterogeneity in the capital regulation-bank risk nexus," Journal of Financial Stability, Elsevier, vol. 8(2), pages 57-68.
    8. Tang Qingguo & Cheng Longsheng, 2008. "M-estimation and B-spline approximation for varying coefficient models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 611-625.
    9. Senturk, Damla & Nguyen, Danh V., 2006. "Estimation in covariate-adjusted regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3294-3310, July.
    10. Jing Sun & Lu Lin, 2014. "Local rank estimation and related test for varying-coefficient partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 187-206, March.
    11. Tang Qingguo & Cheng Longsheng, 2012. "Componentwise B-spline estimation for varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 53(3), pages 629-652, August.
    12. Zhang, Wenyang & Lee, Sik-Yum & Song, Xinyuan, 2002. "Local Polynomial Fitting in Semivarying Coefficient Model," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 166-188, July.
    13. 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.
    14. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    15. R. Carter Hill & Kang-sun Lee, 2001. "Performance of Bandwidth Selection Rules for the Local Linear Regression," Departmental Working Papers 2001-10, Department of Economics, Louisiana State University.
    16. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    17. Wan Tang & Guoxin Zuo & Hua He, 2011. "Double-smoothing for varying coefficient models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 917-926.
    18. Li, XiaoLi & You, JinHong, 2012. "Error covariance matrix correction based approach to functional coefficient regression models with generated covariates," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 263-281.
    19. Kong, Dehan & Bondell, Howard D. & Wu, Yichao, 2015. "Domain selection for the varying coefficient model via local polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 236-250.

    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. Fruth, J. & Roustant, O. & Kuhnt, S., 2019. "Support indices: Measuring the effect of input variables over their supports," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 17-27.
    2. Shi, Jianhong & Bai, Xiuqin & Song, Weixing, 2020. "Nonparametric regression estimate with Berkson Laplace measurement error," Statistics & Probability Letters, Elsevier, vol. 166(C).
    3. Zhan-Qian Lu, 1999. "Multivariate Local Polynomial Fitting for Martingale Nonlinear Regression Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(4), pages 691-706, December.
    4. Francesco Giordano & Maria Lucia Parrella, 2014. "Bias-corrected inference for multivariate nonparametric regression: model selection and oracle property," Working Papers 3_232, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    5. Charnigo, Richard & Feng, Limin & Srinivasan, Cidambi, 2015. "Nonparametric and semiparametric compound estimation in multiple covariates," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 179-196.
    6. Chan Shen, 2019. "Recursive Differencing for Estimating Semiparametric Models," Departmental Working Papers 201903, Rutgers University, Department of Economics.
    7. Giordano, Francesco & Parrella, Maria Lucia, 2016. "Bias-corrected inference for multivariate nonparametric regression: Model selection and oracle property," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 71-93.
    8. Lee, Ji Hyung & Park, Byoung G., 2023. "Nonparametric identification and estimation of the extended Roy model," Journal of Econometrics, Elsevier, vol. 235(2), pages 1087-1113.
    9. Francesco Giordano & Soumendra Nath Lahiri & Maria Lucia Parrella, 2014. "GRID for model structure discovering in high dimensional regression," Working Papers 3_231, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.

    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:74:y:2000:i:1:p:116-134. 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.