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Empirical Likelihood‐Based Inferences for Generalized Partially Linear Models

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  • HUA LIANG
  • YONGSONG QIN
  • XINYU ZHANG
  • DAVID RUPPERT

Abstract

. This paper considers generalized partially linear models. We propose empirical likelihood‐based statistics to construct confidence regions for the parametric and non‐parametric components. The resulting statistics are shown to be asymptotically chi‐square distributed. Finite‐sample performance of the proposed statistics is assessed by simulation experiments. The proposed methods are applied to a data set from an AIDS clinical trial.

Suggested Citation

  • Hua Liang & Yongsong Qin & Xinyu Zhang & David Ruppert, 2009. "Empirical Likelihood‐Based Inferences for Generalized Partially Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 433-443, September.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:3:p:433-443
    DOI: 10.1111/j.1467-9469.2008.00632.x
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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. Liang H. & Wang S. & Robins J.M. & Carroll R.J., 2004. "Estimation in Partially Linear Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 357-367, January.
    4. 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.
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    Cited by:

    1. Rong Liu & Yichuan Zhao, 2021. "Empirical likelihood inference for generalized additive partially linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 569-585, September.
    2. Zhang, Lyuou & Zhou, Wen & Wang, Haonan, 2021. "A semiparametric latent factor model for large scale temporal data with heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    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. Jun Zhang & Yiping Yang & Gaorong Li, 2020. "Logarithmic calibration for multiplicative distortion measurement errors regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 462-488, November.
    5. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.
    6. Zhensheng Huang, 2011. "Empirical likelihood for generalized partially linear varying-coefficient models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1265-1275, May.
    7. Zhang, Jun & Lin, Bingqing & Zhou, Yan, 2021. "Kernel density estimation for partial linear multivariate responses models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    8. Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
    9. Li, Daoji & Pan, Jianxin, 2013. "Empirical likelihood for generalized linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 63-73.
    10. Chen, Qixuan & Paik, Myunghee Cho & Kim, Minjin & Wang, Cuiling, 2016. "Using link-preserving imputation for logistic partially linear models with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 174-185.
    11. Zhenghui Feng & Jun Zhang & Qian Chen, 2020. "Statistical inference for linear regression models with additive distortion measurement errors," Statistical Papers, Springer, vol. 61(6), pages 2483-2509, December.

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