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Optimal zone for bandwidth selection in semiparametric models

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  • Jialiang Li
  • Wenyang Zhang
  • Zhengxiao Wu

Abstract

We study the general problem of bandwidth selection in semiparametric regression. By expanding the higher-order terms in the Taylor series for the asymptotic mean-squared error, we provide a theoretical justification for the earlier empirical observations of an optimal zone of bandwidths in the literature. Based on the idea of cross-validating parametrical estimates, we further introduce a novel bandwidth selector for semiparametric models. The method is demonstrated by numerical studies to be able to preserve the selected bandwidth within the optimal zone. This data-driven cross-validation method may also be applicable for model diagnosis and longitudinal data settings. Examples from two clinical trials are provided to illustrate the applications.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:701-717
    DOI: 10.1080/10485252.2010.533768
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    4. Fan, Jianqing & Huang, Tao & Li, Runze, 2007. "Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 632-641, June.
    5. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    6. 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.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
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    2. Roozbeh, Mahdi, 2018. "Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 45-61.
    3. Roozbeh, Mahdi, 2015. "Shrinkage ridge estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 56-74.
    4. M. Arashi & Mahdi Roozbeh, 2019. "Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data," Statistical Papers, Springer, vol. 60(3), pages 667-686, June.
    5. 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.
    6. Roozbeh, Mahdi, 2016. "Robust ridge estimator in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 127-144.
    7. Xu, Meng & Li, Jialiang & Chen, Ying, 2017. "Varying coefficient functional autoregressive model with application to the U.S. treasuries," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 168-183.
    8. Amini, Morteza & Roozbeh, Mahdi, 2015. "Optimal partial ridge estimation in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 26-40.

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