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Variable Bandwidth Selection in Varying-Coefficient Models

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    4. Senturk, Damla & Nguyen, Danh V., 2006. "Estimation in covariate-adjusted regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3294-3310, July.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

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