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Model structure selection in single-index-coefficient regression models

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  • Huang, Zhensheng
  • Pang, Zhen
  • Lin, Bingqing
  • Shao, Quanxi

Abstract

Single-index-coefficient regression models (SICRM) have been proposed and used in the literature for avoiding the “curse of dimensionality”. However, there is no efficient model structure determination methodology for the SICRM. This may cause a tendency to use models that are much larger than required. In this paper, we propose a new procedure for model structure determination in the SICRM; that is, the penalized estimating equations (PEE) for variable selection that combines the “delete-one-component” method and the smoothly clipped absolute deviation penalty. The proposed PEE method can simultaneously identify significant variables of the index and estimate the nonzero coefficients of the index parameters. We also further study testing for nonparametric index-coefficient functions. Asymptotic properties for the proposed estimation procedure have been established. Under the appropriate conditions, we demonstrate that the proposed estimators have the oracle properties. Monte Carlo simulation studies are conducted to assess the finite sample performance of the proposed methods. A real example is analyzed as an illustration.

Suggested Citation

  • Huang, Zhensheng & Pang, Zhen & Lin, Bingqing & Shao, Quanxi, 2014. "Model structure selection in single-index-coefficient regression models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 159-175.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:159-175
    DOI: 10.1016/j.jmva.2013.12.006
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    Cited by:

    1. Chaohui Guo & Hu Yang & Jing Lv, 2018. "Two step estimations for a single-index varying-coefficient model with longitudinal data," Statistical Papers, Springer, vol. 59(3), pages 957-983, September.
    2. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.
    3. Feng, Sanying & Xue, Liugen, 2015. "Model detection and estimation for single-index varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 227-244.

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