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Corrected empirical likelihood inference for right-censored partially linear single-index model

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  • Huang, Zhensheng
  • Pang, Zhen

Abstract

This article deals with the inference on a right-censored partially linear single-index model (RCPLSIM). The main focus is the local empirical likelihood-based inference on the nonparametric part in RCPLSIM. With a synthetic data approach, an empirical log-likelihood ratio statistic for the nonparametric part is defined and it is shown that its limiting distribution is not a central chi-squared distribution. To increase the accuracy of the confidence interval, we also propose a corrected empirical log-likelihood ratio statistic for the nonparametric function. 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 confidence intervals. A real example is also considered.

Suggested Citation

  • Huang, Zhensheng & Pang, Zhen, 2012. "Corrected empirical likelihood inference for right-censored partially linear single-index model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 276-284.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:276-284
    DOI: 10.1016/j.jmva.2011.10.002
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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. Qin, Gengsheng & Jing, Bing-Yi, 2001. "Censored Partial Linear Models and Empirical Likelihood," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 37-61, July.
    3. 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.
    4. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    5. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    6. Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood for a Varying Coefficient Model With Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 642-654, June.
    7. 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.
    8. Wang, Qi-Hua & Li, Gang, 2002. "Empirical Likelihood Semiparametric Regression Analysis under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 469-486, November.
    9. Huang, Zhensheng & Zhou, Zhangong & Jiang, Rong & Qian, Weimin & Zhang, Riquan, 2010. "Empirical likelihood based inference for semiparametric varying coefficient partially linear models with error-prone linear covariates," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 497-504, March.
    10. Lu, Xuewen & Cheng, Tsung-Lin, 2007. "Randomly censored partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1895-1922, November.
    11. Lai, T. L. & Ying, Z. L. & Zheng, Z. K., 1995. "Asymptotic Normality of a Class of Adaptive Statistics with Applications to Synthetic Data Methods for Censored Regression," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 259-279, February.
    12. Sun, Jie & Kopciuk, Karen A. & Lu, Xuewen, 2008. "Polynomial spline estimation of partially linear single-index proportional hazards regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 176-188, September.
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    Cited by:

    1. 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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