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Statistical inference for the index parameter in single-index models

Author

Listed:
  • Zhang, Riquan
  • Huang, Zhensheng
  • Lv, Yazhao

Abstract

In this paper, we are concerned with statistical inference for the index parameter in the single-index model . Based on the estimates obtained by the local linear method, we extend the generalized likelihood ratio test to the single-index model. We investigate the asymptotic behaviour of the proposed test and demonstrate that its limiting null distribution follows a [chi]2-distribution, with the scale constant and the number of degrees of freedom being independent of nuisance parameters or functions, which is called the Wilks phenomenon. A simulated example is used to illustrate the performance of the testing approach.

Suggested Citation

  • Zhang, Riquan & Huang, Zhensheng & Lv, Yazhao, 2010. "Statistical inference for the index parameter in single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 1026-1041, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:1026-1041
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    References listed on IDEAS

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    1. Ip, Wai-Cheung & Wong, Heung & Zhang, Riquan, 2007. "Generalized likelihood ratio test for varying-coefficient models with different smoothing variables," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4543-4561, May.
    2. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    3. Jianqing Fan, 2004. "Generalised likelihood ratio tests for spectral density," Biometrika, Biometrika Trust, vol. 91(1), pages 195-209, March.
    4. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
    5. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
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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. Melanie Birke & Sebastien Van Bellegem & Ingrid Van Keilegom, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 168-191, March.
    3. Huang, Zhensheng & Pang, Zhen & Zhang, Riquan, 2013. "Adaptive profile-empirical-likelihood inferences for generalized single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 70-82.
    4. Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.
    5. Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.
    6. Ewa Strzalkowska-Kominiak & Ricardo Cao, 2014. "Beran-based approach for single-index models under censoring," Computational Statistics, Springer, vol. 29(5), pages 1243-1261, October.

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