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Semi-varying coefficient models with a diverging number of components

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  • Li, Gaorong
  • Xue, Liugen
  • Lian, Heng

Abstract

Semiparametric models with both nonparametric and parametric components have become increasingly useful in many scientific fields, due to their appropriate representation of the trade-off between flexibility and efficiency of statistical models. In this paper we focus on semi-varying coefficient models (a.k.a. varying coefficient partially linear models) in a "large n, diverging p" situation, when both the number of parametric and nonparametric components diverges at appropriate rates, and we only consider the case p=o(n). Consistency of the estimator based on B-splines and asymptotic normality of the linear components are established under suitable assumptions. Interestingly (although not surprisingly) our analysis shows that the number of parametric components can diverge at a faster rate than the number of nonparametric components and the divergence rates of the number of the nonparametric components constrain the allowable divergence rates of the parametric components, which is a new phenomenon not established in the existing literature as far as we know. Finally, the finite sample behavior of the estimator is evaluated by some Monte Carlo studies.

Suggested Citation

  • Li, Gaorong & Xue, Liugen & Lian, Heng, 2011. "Semi-varying coefficient models with a diverging number of components," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1166-1174, August.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:7:p:1166-1174
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    References listed on IDEAS

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    1. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
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    Cited by:

    1. Zhaoliang Wang & Liugen Xue & Gaorong Li & Fei Lu, 2019. "Spline estimator for ultra-high dimensional partially linear varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 657-677, June.
    2. 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.
    3. Jun Zhang & Zhenghui Feng & Peirong Xu & Hua Liang, 2017. "Generalized varying coefficient partially linear measurement errors models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 97-120, February.
    4. 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.
    5. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    6. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    7. Jun Zhang & Nanguang Zhou & Zipeng Sun & Gaorong Li & Zhenghong Wei, 2016. "Statistical inference on restricted partial linear regression models with partial distortion measurement errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 304-331, November.

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