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Efficient inferences on the varying-coefficient single-index model with empirical likelihood

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  • Huang, Zhensheng

Abstract

The varying-coefficient single-index model (VCSIM) is a useful extension of the existing varying-coefficient model, the single-index model and partially linear single-index model. In this article, statistical inferences for the index parameter of interest for the VCSIM are investigated. By the empirical likelihood method proposed by Owen (2001), two new and simple estimating equations for the index parameter are constructed, then two efficient maximum empirical likelihood estimators (MELEs) of the index parameter are defined. Simulation results show that the proposed MELEs are asymptotically more efficient than existing estimators in terms of limiting variance. Based on the MELE, a new profile empirical likelihood for a single component of the parameter is defined. The resulting statistic is proved to follow a standard chi-squared limiting distribution. Simulation studies are undertaken to assess the finite sample performance of the proposed methodology.

Suggested Citation

  • Huang, Zhensheng, 2012. "Efficient inferences on the varying-coefficient single-index model with empirical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4413-4420.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4413-4420
    DOI: 10.1016/j.csda.2012.03.024
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    References listed on IDEAS

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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    3. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    4. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
    5. Chiang C-T. & Rice J. A & Wu C. O, 2001. "Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 605-619, June.
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    Cited by:

    1. Zhensheng Huang & Xing Sun & Riquan Zhang, 2022. "Estimation for partially varying-coefficient single-index models with distorted measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 175-201, February.

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